Aussies generally knock out a fairly decent English accent; Geoffrey Rush and Guy Pearce (Pom by birth, I guess but moved down under at like four) particularly adept and Russell Crowe (I know he's a kinda kiwi, but we'll gloss over that for now) did a decent RP English in Gladiator, but always says "nut" instead of "not" (Are we nut entertained?) which kinda broke the spell. Americans doing Oirish accents shit me the most. Richard Gere and Tom Cruise particularly offensive in this regard.
Or movies where white guys get into a different culture and become better at it than the natives. Avatar, Last Samurai etc. Fuck off.
Another thing I fucking hate is when Americans play Germans (or another European nationality that don't speak English) and instead of subtitles just speak English in an accent ffs
TBF to Connery he makes no concessions to any character's origins when it comes to accent; he played an Irish cop with the same Edinburgh brogue as he played a Soviet sub captain in The Hunt for Red October and a Geordie NCO in The Man who would be King.
This shits me to no end. There are enough good British actors out there now just cast one of them if your yank can't do it ffs