Hi Nathan,
*** indicates that your created dimension can not find the geometry (edges) that were used to create it. This is one of the reasons for using "show dimensions" that are created in the sketch of the model as they do not loose their association in the drawing.
My guess is that your drawings are not showing the "correct" version (dot number extention) of the model. So even though the geometry looks correct, the actual edges used to create drawing dimensions are not. This can happen when you inadvertantly create a drawing using a model from a different directory - for example after using "back up". So the model in session while creating the drawing is being saved to a different directory.
The "solution" to this particular problem is to locate the correct model (probably in a subdirectory or other directory) and open it into session. Now when you open the drawing, it will look at the model in session and if it is the correct model, the dimesions should appear correctly again. Now use file/back up on the part to get it into the directory with the drawing (or the directory that your drawing is looking). Exit pro/e or use file/erase in session to verify that you have corrected the problem.
Some users don't like to use show dimesions because they find it more difficult and slower, but I have been doing this forever and it does not take longer once you are use to the process. Ultimately it leads to fewer mistakes while creating the drawing. Of course there are times when creating dimensions in the drawing are the way to go.
Best of luck
Scott