The worst kind of incompatibility is one where a program that is legal in Ada 83 is also legal in Ada 95 but can have an effect in Ada 95 that was not possible in Ada 83. Fortunately this is extremely rare, but the one situation that you should be alert to is the change in the predefined type Character from 7-bit ASCII to 8-bit Latin-1.
The range of Standard.Character is now the full 256 characters of Latin-1, whereas in most Ada 83 implementations it was restricted to 128 characters. Although some of the effects of this change will be manifest in compile-time rejection of legal Ada 83 programs it is possible for a working Ada 83 program to have a different effect in Ada 95, one that was not permitted in Ada 83. As an example, the expression Character'Pos(Character'Last) returned 127 in Ada 83 and now delivers 255 as its value. In general, you should look at the logic of any character-processing Ada 83 program and see whether it needs to be adapted to work correctly with Latin-1. Note that the predefined Ada 95 API has a character handling package that may be relevant if code needs to be adapted to account for the additional Latin-1 elements. The desirable fix is to modify the program to accommodate the full character set, but in some cases it may be convenient to define a subtype or derived type of Character that covers only the restricted range.