I believe there are some serious driver issues with the 64 bit vista but I'm sure you would have to search specific to what applications you are referring to. I've been debating it myself and believe I will go with the 32 bit.
Look for drivers for your hardware to see if everything is 64 compatible. For apps, many apps run with no issues, many do not - like stated above, depends on the app. From the different Vista forums, the vast majority of people have issues with apps not being 64 bit compatible and for that reason alone they are sticking with 32 bit (especially for gaming) until 64 matures. However, a very small but growing segment of people are running 64 bit and finding alternatives or stopped using non-compatible apps.
As the other guys said I think you should make sure that you have the proper drivers. Luckily Vista 64-bit drivers exist for ALL my Hardware so i'm using it without any problems and it seems to run a lot quicker than 32-bit Vista. Having run both versions on the same PC I can also say that the 64-bit version seems to be more stable as well. In answer to your question you should be able to run any software that runs on 32-bit Vista on 64-bit Vista because when running 32-bit software they are executed the same way (Windows kind of switches over but i'm not 100% sure how it works). However if you use 64-bit ports of 32-bit software the results are not always great for example 64-bit HL2. Hope this helps.