The performance of a lens at maximum aperture really boils down to two things: lens element material and lens element and group construction. A "lens" as we commonly refer to in the DSLR world is actually a collection of individual glass lens elements, often grouped into related sets. There are a wide variety of type of individual lens elements that aim to control optical aberrations and refract light appropriately so an image can be focused clearly onto the image plane. These lens elements include your standard convex, concave, and partial convex/concave lenses that normally refract light, apochromatic, achromatic doublet, and diffractive lenses designed to correct chromatic aberrations, aspheric lenses designed to correct spherical aberrations, high density glass or glass alternatives used to refract light with less aberration, ultra low dispersion glass to reduce dispersion (and therefor chromatic aberration), etc.
A cheaper lens will use cheaper lens elements, and have fewer correcting groups designed to eliminate optical aberrations such as chromatic aberration, spherical aberration, distortion, and a few others. For cheaper quality f/1.4 lenses, used wide open, you are most likely to encounter chromatic aberration, which usually presents as color fringing. You may also encounter focus shift problems as you stop down the aperture in a cheaper lens, due to spherical aberration. In some cases, spherical aberration is a desirable attribute, as it creates extremely soft bokeh (background blur circles). Such a trait is particularly desirable in portrait lenses. Simpler lenses with fewer elements have the potential to offer superior sharpness, as the more lens elements, the more compromises you will ultimately have to make. This superior sharpness is usually only realized when the lens is stopped down beyond f/2.8, however, due to the lack of correction for optical aberrations at wider apertures.
A more expensive lens will usually use higher quality glass, and include elements with ultra high density/ultra low dispersion elements, apochromatic and/or apsherical lens elements, and possibly lens elements made of flint or flourite. There will often be more corrective groups in a higher quality lens to maximize control over how light refracts, disperses, and focuses. Lens elements in a high quality lens will also sport high quality multicoating to eliminate lens flaring and ghosting, which results in a sharper image than with lens elements that are not multicoated. (Cheaper lenses will usually include multicoated front and back lens elements, but may not include multicoated lenses for all elements.) A top of the line fast prime, while it will still exhibit some optical aberrations wide open, will usually be FAR superior to a cheap lens. The background bokeh of a quality lens is also usually much more desirable as the design of the lens diaphram is usually more advanced as well, with more blades, curved blades to avoid polygonal out-of-focus circles, etc.
When it comes to lens quality, you ultimately get what you pay for. If you need top of the line, wide-open performance, you're going to need a top of the line lens that is designed to deliver top of the line wide-open performance. This would be the case if you were doing portrait or wedding photography for a living, and needed that optimal bokeh at f/1.4 (or f/1.2 even) for superb facial portraits. If you need a fast lens, but will mostly use it for night photography or in situations where capturing supreme focus with ideal background blur is not key factor, then an f/1.4 that has moderate bokeh some chromatic aberration issues wide open will likely not be an issue.
These days, most f/1.8 lenses offer decent quality wide open, and pretty fantastic quality when stopped down past f/2.8 (and up the the diffraction limit of the camera, which usually falls around f/8 or so.) There are a variety of f/1.4 lenses from several brands, ranging from pretty cheap to really high quality. A middle-ground f/1.4 lens can be had for about $500 or so that will deliver very acceptable quality wide open, and better stopped down a bit (most lenses improve in sharpness when the aperture is closed down by a stop or two.) If you want the best quality as wide as you can get it, most big name brands like Nikon and Canon, as well as Zeiss, make very expensive, very wide lenses (as wide as f/1.2) that offer unsurpassed quality from their widest aperture through f/2.8, and possibly beyond. You'll have to pay for this quality, though, as these lenses usually roll in for around $2k.
An interesting consequence of achieving maximum wide-open quality, however, is often less than maximal quality through the "middle" aperture range, from f/2.8 through the diffraction limit. Compare a cheap $90 nifty fifty f/1.8 at f/4 to a $2000 f/1.2 at f/4, and the cheap lens will probably edge out the expensive lens in the area of sharpness. The additional and non-standard lens elements (like apochromatic, aspherical, etc.) can correct optical aberrations wide open, but usually at the cost of some sharpness. The higher quality lens, despite having slightly lower sharpness, will still usually provide superior color, contrast, and clarity.