Well, the only thing limiting the current to the LED would be the 1K resistors to the +5 and Gnd rails. The divider creates a 2.5v tap with 1K of resistance either direction. That sounds current-limited to me. 
I'm still at a loss for why the probing caused things to change. For that matter, even on the "actual" project breadboard where things otherwise seemed to work just fine, sometimes just touching (only) the black probe to Gnd would cause the uC to reset. Not always, just sometimes.
I'm honestly not sure how "clean" the power is from my little 3-voltage wall-wart supply. It appears to have its own capacitance because all the LEDs on my project fade out when it's unplugged, but for no reason in particular, I didn't put any large electrolytics on this project board like I usually do. There are ceramic caps on the supply pins though. I don't suspect loose connections per se, since it doesn't appear to mind being jiggled or touched.
Thanks for the brainstorming, everyone. This one might remain a mystery though. Well, just for fun, here's a pic of the project board. Everybody loves gratuitous breadboard pics, right? The Tiny is the top right IC next to the single green LED.
