Yes, lenses designed for digital sensors have several differences from their older film based camera lens counterparts. One of the primary differences is that digital sensors are more reflective than film, so anti-reflective coatings are applied to the rear element of a digital lens. This helps prevent reflections off the sensor that could result in image ghosting.
Additionally, digital sensors require light to travel down a narrow tube produced by the stack of filters (color, AA, etc) that lie directly in front of the actual photosites that convert the light energy hitting the sensor in to an electronic signal. This alters the way that the light needs to be directed to the sensor (it needs to come in from more straight on) and digital lenses may be designed to handle this better.
Finally, as Michael Clark pointed out, film didn't generally lie perfectly flat, while digital sensors do, so there is more emphasis on extreme levels of sharp resolving power on good digital lenses than film cared about.
It isn't generally a problem to use an old film lens as long as it is compatible with your camera mount system, but it is good to understand the caveats that they can have ghosting problems when shooting in to light, they often have lower sharpness and may have additional chromatic aberrations. They also tend to be older, so they may lack some of the more recent advantages in terms of focus motors and control.
My general recommendation if you are buying new and can afford it, then buy a modern lens, but if you need the capabilities of an expensive lens (such as a fast lens) cheaply, then it may be worth picking up an old film lens and working around the limitations, just make sure to research the particular lens you are looking at and how it compares to other lenses of both similar prices and similar aperture and focal length.