Sweating is always a problem for me.
I sometimes take spin classes and there is one instructor that always comments on how much I sweat: "Look at how much Barbara is sweating! Wow, she really sweats a lot!" I kid you not!
On Thursdays I take a circuit training class that involves also sorts of crazy stuff. At one class, we were crawling around on the floor and I accidentally put my hand down in a sweat pool. I was totally disgusted and it didn't help any when I realized that I was probably the one that created it. And then, just today, someone in the class commented to me on how sweaty and gross the floor was and, as I stood there with sweat literally dripping off me, all I could think was that I was probably the biggest contributor to it.
I have to make sure all of my workout pants are black and don't show any change in color when they are wet with sweat. Otherwise, halfway through my workout it looks like I've peed my pants.
I also get really red in the face. This morning I ran intervals on the treadmill and, afterward, one of the regulars at the gym saw me and said: "Wow, you really have a sun tan!" Oops, no, not a tan--I'm just that red in the face from exercise.

Give me fifteen minutes and I'll look as pale as ever.
I've also had a few inadvertant "gas explosions," usually when doing ab exercises.

Those are the absolute worst in terms of embarrassment.
And then there are just the stupid clumsy things I do, like hitting myself in the chin with the weight bar. Luckily, I haven't managed to injure myself seriously yet. Once my trainer and I were doing an exercise that involved him throwing a medicine ball to me and me catching it; I missed the ball and it completely hit my head. That was pretty funny.
