The main thing I see students doing incorrectly is rushing through it. Go slow at first. There are a few things to keep in mind, and they may seem obvious;
Don't separate the strokes. Let the pick "fall" from string to string. Think of it as dragging, or pulling the pick when doing upstrokes, and pushing the pick for downstrokes.
It's as much a left hand technique as it is a right hand technique. Students frequently use illogical fingerings and position shifts when attempting arpeggios. If you are doing a stock A minor shape starting with your pinky on the A string, the best fingering is: A12 pinky, D10 middle, G9 index, B10 middle, E8 Index, E12 pinky, E8 Index, B10 MIDDLE (not ring, which many players try), etc. Having consistent fingerings is very important. If you want to turn a shape around with two notes on the top string, you may want to utilize slurs for the turnaround, and let the picking resume on the B string. Resist the urge to speed up during the top portion of a shape. Uniform rhythm is important during the learning process.
Go slowly, in time with a click. Try specific rhythms, such as quarter notes, eighths, sixteenths, and then triplets. In case you don't know, Quarter= 1 note per beat, Eighth= 2 per beat, Sixteenth = 4 per beat, and eighth note triplets are 3 notes per beat. It's very common to try to rush through arpeggios with no rhythm, and it just sounds cluttered.
I personally feel that arpeggios sound best at a moderate tempo. Let people actually hear the notes you choose, and the effect will be more interesting.
As far as note choices, attempt more than triads and diminished 7 arpeggios. There are many, many great arpeggio sounds that aren't commonly utilized (sevenths, sus2 and 4, Major and Minor 9, Minor 11, Dominant9,11,13, altered dominant, sixths, etc.)
If you are already competent with triads, you can get 7ths and extensions simply by tapping a high note on the E string. It's a very common technique, but most players tap notes that are in the triad (root, third, fifth), but there is nothing stopping you from tapping more interesting intervals (9th, #4, 13th, etc).
To get arpeggios sounding clean with a lot of gain, you may want to utilize the neck pickup, and be cautious when sweeping near a harmonic node. When you take a finger off of a harmonic node (12th, 7th, and 5th frets, for instance) at high gain levels, it's very easy to get an unintentional harmonic. A simple hair tie around the neck can remedy this, if no amount of effort seems to alleviate the problem.
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It pisses me off so much, I practice and practice but I just cant do them.
