The symptoms of heat exhaustion include feeling faint/dizzy, possible headache and nausea, sweating, and being pale. if this occurs in a diabetic person, what are the chances of this being mistaken for hypoglycemia? (Obviously measuring your blood sugar could give you the answer, but let's forget about that for a moment.)

Yes, that is possible, at least from my own experience. I have mistaken the two conditions on a couple of occasions.

For example, I was out in 100 degree heat a couple of weeks ago, playing soccer for my club team, and I started to feel those symtoms. I was sure I was getting a low blood sugar, so I checked and was 180. after I relaxed for a bit and drank water, I felt fine.

You mentioned it in the question. the only answer is to check your blood sugar.