What is the difference between 1) He was seen to enter the restaurant. 2) I was seen to jump on the bed. and 1') He was seen entering the restaurant. 2') I was seen jumping on the bed. ?Feel free to just provide example sentences.

They are all grammatically correct. There is a small class of verbs like “feel,” “see,” “observe,” and “overhear” that can take either a “to” infinitival or the “ing” form — and for that matter, a perfect. The difference in use/meaning is that the progressive”ing” form emphasizes perception of the act actually occurring, whereas the “to” form is concerned less with the matter of sensory perception of the event in progress, and more with the fact of the event having occurred.

The Cambridge Grammar is the English Language notes that “He had been seen driving. So nobody would ride with him” is sensible; whereas “He was seen to drive. So nobody would ride with him” lacks logic, as would "he had been seen to drive, so ...."

You can find related examples in the CGEL pages 1236-1244. They include “Kim was seen to leave the bank” and “Kim was seen leaving the bank.” Also “he was heard to lock the door” and others. So yes, they are correct in careful writing for a particular nuance of meaning. But it is also true that their meaning is specialized, and most people who don't have occasion for very careful writing will, in daily conversation, where they're mainly concerned with reporting of sensory experiences and not about nuances related to evidence, simply only ever use the latter two forms, with the “Ing” forms.