It's hard to answer this, so I'll focus on the points you listed, except the third because I don't get it/remember.
The execution of Buckbeak
Buckbeak attacked Draco, and he told his father, Lucius, who happens to have great influence in the ministry (this may be a sign of corruption).
... BUT, if you think about it, Buckbeak did bite a young student (although it was Draco's fault). It is not unreasonable to tag the creature as dangerous. Execution may be a bit too extreme, though - however, this may be a sign of a super strict and firm ministry rather than a corrupted one.
Umbridge's appointment and methods at Hogwarts
Umbridge just followed the orders of the ministry, so technically she didn't do anything wrong. She's just ultra insane with an obsession for status - but technically she's not trying to crumble the system or support Voldemort.
The denial and cover-up of Voldemort's return for so long
This was done in a pitiful attempt to maintain Fudge's reputation - yeah, probably adds up to a corrupted system.
Harry's trial for underage magic
Umbridge sent the dementors. Her intention was revealed to be that she was doing her best to shut Harry up - remember that it was the ministry's prime objective to hide all information about Voldemort, so Umbridge just did her best to accomplish this objective (very extreme and insane however). She didn't do it to help Voldemort though.
First of all, the Ministry has had some Death Eaters infiltrated. And Lucius as well. This of course affects the way things work in the Ministry.
Then, it was obsessed with keeping its reputation (Fudge and Umbridge). It's up to you to judge if that makes them corrupt or not (probably yes since they endangered everyone by shutting up Dumbledore).
And finally, it has some insane high-ranking staff like Umbridge. But she's just crazy.
Conclusion? Comparably, it is a pretty standard government...