Which patterns do I have to avoid when modifying the 3'-UTR?
If your goal is to avoid regulatory elements, I would not believe any prediction program, since new regulatory elements are found every day.  The best way would be empirical and just clone and infect with a mutated 3'UTR and see if your gene's regulation is perturbed.  You could at least swap the entire 3'UTR with that from another gene to see if there are even any gene regulatory elements in the 3'UTR.