I installed my first compression fitting (fridge water line) and when I was all done I discovered that it looks like it is slightly crooked. I'm not sure if this means that I bent the pipe or perhaps did something wrong with the compression fitting itself. I finished it all up, turned on the water, checked very incredulously, and found that it didn't leak. I'm definitely going to keep an eye on it for a couple days, but I also can't help wonder if I should just cut it off and try again with a new fitting (there is plenty of room on the pipe). Any guesses if this is okay or a sign of a problem? In case it isn't obvious, this is my first attempt at plumbing.
If it doesn't leak it's OK. It looks square where it goes into the compression fitting.
BTW you didn't need any Teflon tape, but leave it alone now. Teflon tape or pipe dope is used to seal pipe threads exposed to fluid under pressure. Certainly in the compression fitting the threads are used to compress a soft metal seal against the tubing and against the harder metal of the fitting; the threads don't have to be water tight.
With the brass adapter to the flexible line, I believe there is a rubber seal in the flexible line that the brass fitting seals against.
The classic junction requiring sealing of threads is normal pipe threads (NTP), also called IP for iron pipe even when the material is not iron or steel.