Does anyone know whether a bathroom exhaust fan designed to be installed in a ceiling would have any problems if installed in a wall instead? From a mechanical, ball bearings, noise perspective. Not a space perspective.
In my experience, most decent exhaust fans are dual rated, ceiling or wall. If your fan is described as a ceiling mount only, it is probably one of many inexpensive units that use plastic bushings instead of sealed bearings. If you can easily jiggle the fan blade or squirrel cage axle in it's end bushing mounts, then I probably wouldn't waste my time using it in a wall. If it is a common overall dimension (10"X10") for example and the mechanical connections feel tight and smooth, I might give it a try. Hook some power to it and give it a test run horizontally before you install it. The worse case scenario is that you may have to replace it with a more expensive unit at some future time, which is a very easy job assuming the hole in the wall is the same or smaller than the one you need for your existing unit. The easy answer is to simply spend 50 or 60 bucks and buy a new fan rated for wall mounting. I almost forgot to mention, the orientation of the air back flow preventer is very important. If this flapper will not close by gravity or spring when wall mounted then don't consider using it.
Would it not be better to simply purchase a fan designed to be installed into a wall?
It may well vary from fan to fan but all the ceiling exhaust fans I'm familiar with don't really like being mounted vertically. They are normally designed to correctly load their bearings only when ceiling mounted.
If you do mount them vertically you can expect the bearing to wear faster, which means that although they may not sound louder at first, they will get loader as the wear takes place. In some case the shaft may even rub against the plastic body if gravity is not holding it in the correct running location. Those will definitely be louder, even right from the start.