Sharpness is a factor intensely related to viewing context. To use more laymans terms, how sharp a photograph looks greatly depends on how large it is viewed, how closely it is being viewed, how well it is lit (if not on a computer screen), and the visual acuity of the viewer. As such, it is very difficult to judge sharpness without a proper context.
First and foremost, be keenly aware of the differences of viewing a photograph at 100% scaling on a computer screen (especially a nice, large, professional grade screen that is properly calibrated!) The act of examining the image quality of a photo at 100% scaling (usually referred to as 100% crop) is called pixel peeping. Pixel peeping, amongst other things like eye fatigue and neck pain, is one that will lead down the deep, dark, endless rabbit hole of IQ Worry! Humor aside, there is a very big difference between IQ (image quality) at 100% crop and IQ of a fully processed photograph that has been cropped, scaled, de-noised, and sharpened to your liking for your desired presentation medium.
Pixel peeping has its place, and when used properly, is an extremely valuable technique in the digital photographers post-processing toolbox. Its helpful to view a photograph at 100% when removing noise, as noise tends to be "absorbed" by downscaling (i.e. viewing a photograph at less than 100%). It is also helpful when analyzing a photograph for lens aberrations or other defects that might affect IQ, such as spots from dust on the sensor, etc.
The Reality of Image Quality
Image quality, of a landscape, macro shot, or anything else that depends on high detail definition and sharpness is a bit of a chimera, a highly subjective thing that has real-world, mathematically definable bounds. (Contrasted with say portraiture, wherein a little softness and thinner DOF is actually a very desirable thing.) Image quality is dependent upon intrinsic factors, such as sensor resolution, focus, camera shake, as well as extrinsic factors such as presentation medium, viewing distance, and the visual acuity of the viewer.
Intrinsic factors definitely play a role, however how much they affect IQ outside of the realm of pixel peeping can be affected by extrinsic factors. A lower resolution sensor will be less capable than a higher resolution sensor at capturing all the detail in an image that has fine detail...such as a landscape shot containing lots of trees and other flora. The resolution of the lens used at the aperture shot at will also play a role, imposing diffraction limits on the maximum amount of detail that can be physically resolved. The presence or lack thereof of image stabilization technology, or the steadieness of the photographers hands if handheld, can also play a role in sharpness. How well the photo is focused will most certainly play a role, however it is entirely in the hands of the photographer, and is thus a controllable factor. These all impose a physical limit on how much intrinsic sharpness exists in a photograph.
Extrinsic factors can determine whether the intrinsic sharpness of a photograph will affect the final presentation format or not. In the most common cases, intrinsic factors like resolution, camera shake or defocus rarely have an impact unless they are fairly severe. In less common cases, usually in the case of prints blown up more than two times the native size of the photograph, small factors can be enhanced and become more apparent.
Common Presentation Formats and Relative Sharpness
In the general case, most images are viewed at significantly reduced size relative to their native size (100% crop size). This is true for both print and digital viewing mediums.
When published to the internet, the most common presentation size for the largest image dimension ranges between 500 to 900 pixels. With the average image size for modern high megapixel cameras ranging from 4000 to nearly 6000 pixels in the largest dimension, that makes the common internet presentation format about 5-12 times smaller! Sharpness when scaling down so significantly is rarely a problem, and what may be observed as marked softness or blurrieness when pixel peeping will most likely be entirely absorbed when downscaling. Additionally, when downscaling by such a large degree, a significant amount of noise will usually be absorbed, entirely nullifying what may appear to be detrimental degradation of IQ at 100% crop.
When publishing to printed mediums, the more common presentation sizes tend to be smaller than how large the image may be at 100% crop on a computer screen. With the highest megapixel cameras today, native print size is as large as or slightly larger than 13x19" at 300ppi. On top of that, print resolution tends to be 3-4 times higher (more dense) than computer screens. This is where human visual acuity comes into play, which clocks in at around 300-360ppi for an average print (say 8x10 - 13x19) viewed at a proper viewing distance (say a foot and a half). At such resolution, what may appear to be intrusive noise, problematic optical aberrations, or detrimental diffraction softening will generally be beyond the ability of human sight to recognize.
Less common presentation sizes include enlargements. Unlike reductions or prints at native size, enlargements can exacerbate IQ problems visible when pixel peeping. Keeping in mind that the average printer resolution is 3-4 times higher than a computer screen, it usually takes about a 3-fold enlargement for a printed pixel to approach the size of a computer screen pixel. Enlargements up to around 2x or so are usually devoid of any noticeable issues with sharpness or problematic enhancements to optical aberrations or noise. Enlarging a photo beyond 2x, however, will most likely make all the defects visible at 100% crop visible in the print, and put more pressure on the photographer to capture a sharper photo on site.
What is Sharp Enough?
The enhancement of IQ detractors when enlarging doesn't spell the end of the world, however. Scaling for enlargements greater than 2x is usually done with a fair amount of care, with meticulous attention paid to noise and finely tuned sharpening adjustments added. Enlargements do put greater pressure on the photographer at the time the photograph is taken to maximize sharpness. If you do not intend to enlarge, then the diffraction softening from an f/16 aperture on an APS-C camera is most likely a non-issue. I've often shot landscapes at f/22 on a relatively lower resolution Canon 450D, where I know for a fact that diffraction is affecting IQ, and its never been a problem in prints up to 17x22.
Diffraction at f/16 for a modern DSLR (APS-C or FF) is probably of least concern, as achieving perfect focus and ensuring no camera shake are both likely to be the primary detractors to sharpness. Minor effects of chromatic aberration are also usually a non-issue for most presentation formats, however they do have the tendency to make post-process exposure tuning and sharpening adjustments produce funky double-edges to finer details like tree branches, mountain/sky borders, etc. Scaling for internet publication will usually absorb it, however medium sized prints may exhibit issues.
If you do wish to enlarge your photos in print, the camera might already be outresolving the lenses. More important to improving image sharpness in the camera is high quality glass that is capable of resolving fine detail throughout its focal range. A higher resolution sensor will also help, and finding one in a larger format will help even more. A staple of many landscape photographers is the Canon 5D Mark II with either the 17-40mm L or 16-35mm L lens. That combination ensures that the lens is resolving enough detail for the sensor, and that the sensor is large enough to support a high resolution (in this case, 21.1mp). The issue is that the 5D II + L series lens is about a US $3200-$4200 investment.
A top of the line 5DII with an L-series lens is not necessary to get sharp landscape photographs. A canon 550D, 600D, 60D, or 7D with the EF-S 10-22mm lens will also do the job quite well. You won't have the ability to create huge enlargements that can be viewed within a few feet like you might with the 5DII and a 16-35mm lens, but you should be able to produce prints up to 17x22, or any size smaller than that, as well as any format for presentation on the web, without any need for concern about sharpness beyond the factors you can control in-camera.
UPDATE: What Details Matter?
In response to the updated question about whether small details matter. That is really a matter of composition. When it comes to landscapes, whether you see bark on a tree trunk or not, or the veins in the leaves, is entirely about how the scene is composed. Most landscapes are about capturing, in breadth and depth, an amazing landscape. Landscapes, given their expanse, usually do not contain much room for finer detail like bark or leaf veins. In some cases, particularly with ultra wide angle lenses, you can compose such that you get very close to and capture a lot of detail in the very near foreground (rocks, the shore of a lake, a tree stump or fallen tree, etc), while still capturing the greater expanse of a landscape in the background. In such a composition, it would be important that foreground detail is sharp and clear. That is all about focus, and in many cases you can focus such that the foreground is crisp and clear, and the backdrop of the landscape is just on the edge of sharp, but still within DOF enough that the average observer won't notice the slight softness of details way off in the distance.
There is no simple rule you can follow regarding what details matter in a landscape. Generally speaking, fine details are not as important as the whole scene, however when photographing with wide angle, near objects and their detail may be important...its ultimately a matter of choice on the part of the photographer.