This is two issues, but they're closely related.
Firstly, the code completion window obeys the font size as it was when BlueJ loads up. This leads to a slightly confusing sequence of events:
1. Change font size from 12 to 24 (e.g. when on a projector).
2. Show code completion (i.e. hit ctrl-space), and the dialog shows a 12pt code completion dialog.
3. Quit BlueJ, load it up later and switch font size back (e.g. when you go back to a normal monitor after the projector).
4. Hit ctrl-space, and the dialog now shows a 24pt code completion dialog until the next restart.
Secondly, when you do change the font size to 24pt and have the dialog show up properly in 24pt font size (which is useful for showing off the code completion on a projector), the actual code completion window is the same size as usual, meaning most of the display is cut off.