Did Brody get his job back at the end?

No

They better rehire him. If for no other reason than to keep him quiet. They fire him, he goes back to the main land and sells the story of ANOTHER great white shark off the coast of Amity. Two great whites in less than five years and Amity Island is sunk. Keep him on as chief on the condition that he keeps the whole thing quiet and the story never leaves the island.

I dunno. Do you think any of the Council Members resigned in shame over their intransigence and inaction?

I'm assuming he did, given that his son (Sean) had pretty much inherited his job in 'Jaws - The Revenge' (plus his picture was still hung up in the police station)
Had he remained sacked (since 'Jaws 2') despite defeating another killer shark (that only he believed existed) and not given his job back....I doubt his son would have been employed in the same department?

I watched the movie last night and think the ending is a bit rushed. In Jaws 2 we see a lot more of the shark during its attacks, rather than the minimalism of the first movie.

Because of this I feel we should have seen more than the ending we got, something like:

Brody's wife spots a fleet of boats coming back to the docks and jumps in a small dingy to intercept and be with her family, and walk them off onto the docks. There, the politicians make Brody out to be the hero again for the news cameras which just arrive also, and Brody and family brutally reject them, get in his police 4x4 and drive off back to the station where Brody goes into his office, grabs his police badge and gun and the other police guy welcomes him back. He asks Brody what his first orders are and Brody says to tell the mayor to get his ass in his office now. The other guy smiles and goes off. Brody's family watch him sit back in his chair like he owns it again. Zoom out from the police station to reveal life goes on around the island.

I would presume the mayor and all his cronies would face incredible backlash for they're actions! Brodie would be seen as a hero all over again !

For the mayor etc to dismiss brodie after what happened first time , wow I would not like to be in the mayor and the council members shoes ! Would probably have to go into hiding !

yes in jaws 4 you see sean brody as sheriff there is no way he become sheriff if his family name is still black ball. he obviously take the rains from his father.