No, removing the screen is not rocket science, but here are the hazards:
- Introduction of dust into the pentamirror assembly and the inside surface of the ocular (eyepiece)
- Damage to the screen from handling
- Loss of shims
As alluded to above, the best practice is to avoid touching the surface of the screen. It is very fragile. Dust is best removed using a rocket blower (NOT canned air!) with the screen in the camera.
Completely off the record, YMMV, no liability, and every other possible disclaimer, you can try using a cotton applicator swab (Q-tip) saturated with a quality lens cleaning solution to remove finger prints and similar gunge. Do not use alcohol or other solvent. Do not scrub. Follow with a rinse of distilled/deionized water and air dry. This should be done with screen REMOVED from the camera. Now how heavy gunge might have gotten on your screen shall not be discussed as it is potentially embarrassing.
And finally...
Some dust in the viewfinder is inevitable. Learn to live with it.
Steve