Recently, a worksheet that I have used for several years (in Excel
2002)
started having odd behavior when I save it. It started when I
clicked the close button, and instead of prompting with the typical
save dialog box of yes, no, and cancel, it instead opened a "save as"
dialog box with a file listing.

Ever since, it has behaved oddly and inconsistently regarding saving.
Sometimes it has started the "save as" function, and other times it has
shown a series of the save dialog boxes one after another (weirdly
enough, the extra ones seemed to be in a different font than "good"
dialog boxes of a similar kind).

My best bet usually is to save the worksheet and then close it. Often
avoids the problem (albeit with an extra step), but sometimes it
doesn't.

Is there a place that I can go looking to debug this issue? This is a
critical worksheet, and I don't want this to be a sign of other
problems to come.