Keep in mind, I was only 19-20 years old during my summer of nonrev, so I think if I dressed up too much it'd probably be a little strange. Plus, I only once even tried to get into first class (ANC-MSP redeye) but didn't get it anyway.
That said, I usually wore collared polos if I WASN'T flying, and that seemed to work out ok on the flights. This was never really brought up as an issue when we were told about our flight privileges, but it'd come up in conversation sometimes at work. I think I may have been pushing it a little, but it was only brought up once, and barely. I was wearing a t-shirt this time, (actually, I think I'm wearing the same one right now) trying to get listed for an earlier flight from YYZ-DTW. The gate agent was really friendly about it, was shocked that my seniority was only about 2 months. He told me that "as someone that's worked here for a long time, it's always best to dress up for first, since you never know if that's all that will be left. If you're not dressed for the part, and that plane is about to go, you risk it flying without you" but since I was in coach, it wasn't a problem.
Another time, I was flying from MSP-SEA. I sat next to a guy on a buddy pass going from LAS-MSP-SEA to see his brother. He wasn't dressed very well to begin with, and the gate agent at MSP said he needed a collared shirt, even in the back. He was able to get one at a shop at the airport, at least.
I also heard a story from someone at work years back: She was trying to get a flight home from NRT (or maybe to NRT, then home, I forget) and was overall pretty well dressed. The only problem was, her dress shoes were in her checked luggage and the gate agent was VERY picky. She wouldn't let her on the plane without better shoes, and I think for some reason buying them in the airport was not an option. Desperate to get on that flight (other options were limited, and there's a good chance she'd have the same gate agent anyway) she ended up talking with a pax who agreed to switch shoes during boarding. When the gate agent saw that, she glared at her (understandably, but options were very limited at that time). It wasn't until the plane was airborne that my coworker dared to trade shoes back
