This concerns AN2, not AN.
The text in-game is too large for the various dialogue screens, so some bits overlap and other bits get cut off by the dialogue windows.
So far it's been a purely cosmetic issue, and perhaps it will remain so. I wouldn't know, I've only played through the first tutorial so far.
It's annoying, however. So does anyone know what to do about it? It does not appear to have anything to do with screen resolution, so I'm guessing it's font related. But that doesn't help me solve it.
I'm running it on a WinXP machine.

my guess and suggestion would be , try to run it in a windowed mode.
If the text doesn't scale like it should , and it keeps overlapping we indeed have a font problem on our hands.
So first try running in window mode.
Also give us a bit of info on your system.
Do you have an LCD monitor?

I've got this problem too. I'd say it's a little more serious though, since I can't read all the instructions the bird-guy gives. I mean, I can probably figure it out on my own, but I shouldn't have to play guessing games with instructional text.

Here's my specs:

Intel Core 2 Duo E7300 running at 2.66ghz each, 6GB of Ram, Windows 7 64-bit
I've got a Radeon HD 6850 with 1gb of video ram.

i've tried running it in various compatability modes and I've tried some different resolutions but no dice.

Same here. I am running it in Windows XP 32-bit, and I have tried

1) Compatibility mode for Windows 98/ME
2) different resolutions (standard 800x600, and several widescreen resolutions)
3) fullscreen and window mode

In every mode, the text is too big, and e.g. the tutorial mission text is cut at the bottom of the message box. (Also other text is cut, like the "own buildings destroyed" in the score screen.)