Banjo took the word right out of my mouth.
A dialect differs in vocabulary and grammar from the standard variety. An accent differs only in pronunciation.
In my experience there are definitely different dialects AND accents in ASL.
Oh my gosh! Accents, accents, accents!! I'm in ASL Level 2 at the local Deaf Action Center, and we've had 4 separate teachers in about 8 weeks (they just moved to a new building and they're having some logistics problems!). The accents are driving my crazy! One of my teachers always turns his 'E' parallel to his gaze direction, so if you happen to be sitting to his right, you cannot tell whether he's signing a 'C' or an 'E'. He also doesn't curve his hand for his 'C', so that makes it look even more like an 'E'. I've started to get used to it now, but the first couple of days I was getting SO frustrated.
The other interesting thing I've noticed is that even deafies who live in the same community don't always agree on which sign best means a given concept. Sometimes you'll have a word that's very similar in meaning to another word (for example: idea, thought, concept, imagination, invention -- all of them are sort of related), and I've learned they'll disagree on which sign means which English word ("Protest" and "strike" seems to be another one I stumbled upon the other day). I figure it's all good -- you don't learn a foreign language by only learning one word for each concept, so just tuck them all away for future reference and try to figure out what the people you're signing with use.
Today I spent the afternoon with some deaf senior citizens at a local Deaf church -- playing cards and dominos. Man, they use many different signs than my teachers. They also don't like a lot of the signs I've been taught. There's some kind of ASL cultural divide between young and old signers. It seems like around 80% of the signs are the same, but you get some funny looks every once in a while. Then you get a kind of "light bulb goes on" look, and a frown and then they'll sign something like "new sign, we don't use".
I really love learning ASL. It's such an expressive way to communicate. I can't wait until I'm really fluent. I wonder what the word would be like if all hearies learned sign just like many learn a musical instrument. It seems like a lot of misunderstandings could be avoided if we hearies could use both speech and sign at the same time, even in regular speaking conversation.