Bang On!

Morons,

Johnny Depp's accent was bang on. Those who say otehrwise are either daft foreigners who don't understand or appreciate the subtleties of English dialect - old dialect at that - or are even dafter Brits who should know better.
Beyond this are those who want to take pot shots at Johnny Depp (out of jealousy?) or are numb Brits who like to gain an air of superiority over anyone "daring" to attempt an English accent.

For the most part, the pirate accents in the film were based on those at the time of pirates, namely South Western England (Dorset, Bristol, Southampton) and a bit Eastern with Cornwall and co.

This accent was exemplified by Captain Barbosa.

Johnny Depp is one of the few who can pull off a variety of English accents from East End (From Hell) to RP (Sleepy Hollow) and to common scallion (Pirates of the Caribbean).

His accent is a mish mash of the 'traditional' pirate accent and a common London accent. This latter being the stronger of the two. Yes, it is played up. Partly for effect and partly because accents were stronger back then.
Indeed, in the 1500's for example, the Bristol accent was even stronger than it is now and was close to being indistinguishable from Irish.

As a Brit who knows teh history of language, I know what I'm talking about.