Question: I get this really bad feedback sounding noise when I play stuff like this, from the beginning of the Free Bird solo, 
shown in tab:

```
1  ----18---18---18---------
2  -18---18---18---------

```

(All notes on second string played with a full bend.)

It's there on any amount of distortion, but not when I play clean. Is it a problem with the amp? If so, what can I do about it?

Answer: 
This could be a number of problems. 

1. Dissonance: This, in basic terms, is when two notes do not sound good together, and clash producing an unpleasant noise. However I have tried this out on my guitar and amp and I do not get any dissonance, so it may not be that.
2. Amp/Speaker Problems: I have found, particularly with Line 6 Amps and Speakers, that when the bass and mid knobs are turned very high, the speaker cannot cope very well and produces and grinding feedbacky boom.
3. Tuning problems: It may sound stupid and patronising of me, but are you perfectly in tune? According to both ear and tuner? If so, your guitar's intonation may be out. Any slight fault in an intonation setup causes the guitar to be out of tune with itself, and therefore notes that usually harmonise well may suddenly sound dissonant. This is greatly accentuated at higher frets, where strings will sound even worse if the intonation is out.
[See this previous question](https://music.stackexchange.com/questions/1604/what-is-intonation-and-how-can-i-find-out-if-my-guitar-has-correct-intonation) for help about intonation.

Distortion greatly increases the unpleasant dissonant sound, so that may explain why you do not find you have the problem on a clean setting. 

Hope this helps.
Before "throwing out" your Amplifier I would suggest trying a different guitar! A good guitar with good mics will sound at least resonable through a bad amp, while a bad guitar will sound crappy even through the best amps. I looked at some reviews of your guitar since I am not familiar with that model and it seems like feedback noise is something that many people get with it... A more expensive amp will probably not fix your feedback issues either since the problem lies in the wiring of the mics.
Hope this helps!

"It can't really handle being cranked through an amp too loud because it feeds back and isn't made for anything huge"
<http://www.ultimate-guitar.com/reviews/electric_guitars/first_act/me300/index.html>