Is the following a film flaw?

Nope, I'm Brazilian and I was always confused by this, also. Can't say I know anything about the military police, honestly (just that they're corrupt, I'm afraid).

The recruit will fill out his vacant job but won't inherit his captain position, another veteran will most likely. He just want the new recruit to be up to his standards and eventually succeed him as captain like we see in the sequel.

yeah, that made absolutely no sense to me, as well.

I'll try to explain:

Part 1:

For you to work for Government in Brazil, you have to take a public exam. Government publishes how many vacancies are, how much they pay, the day you do the test and then you subscribe. It's like the SAT exam, but for careers.

Part 2:

It will be difficult to explain the brevet in english but.. i'll try.

There are two types of carrer in the Brazilian Military Police (so, two kinds of exams): Official/Officer and Soldiers (enlisted men, servicemen).

Soldier is the base and the most numerous. You can only upgrade to "Cabo" (i think it's 'corporal' brevet)

Official/Officer is that one for commanders/rulers. You start as aspirant (as Matias and Neto was), then you can upgrade for the others brevets, like Cpt , colonel, etc(it's a really big chain).

In general, a group has at least one Officer (in this case Capt Nascimento) to command the squad/troop.

Getting it to the movie: Cpt Nascimento was the officer of his squad and he could only be replaced by another person in the Officer carrer. All the other guys in his troops were in the soldier career.
That's why he was looking for an aspirant (who wasnt contaminated by the system) to be his recruit.

Nowadays, soldier carrer doesnt need university degree but Officers carrer do.

If Capt Nascimento's men would like to join Officer carrer, they could, but they had to be approved in the Officer exam and classificated in the number of vacancies.

Got it?
Sorry for any english mistake.

It makes no sense to you in your nice apartment

I believe Matias and Neto were both new lieutenants. Their ranking system is the same as the military, people who attended university or took the officer course could jump straight in as junior grade lieutenants and lead men or departments. People who had no college education would have to enrol at the bottom ranks like private etc.

Thats why Neto was assigned to the motor pool and Matias was in charge of the records. I believe that all the recruits who tried to join BOPE in the movie were all Officers ie lieutenants and above, there must be a separate recruiting session for the grunts which we don't see. Matias and Neto would join as lieutenants into BOPE and probably lead a squad and eventually get promoted to captain and lead more men.

Another thing I would like to clear is, In my country you can't join the police or army if your eyesight is weak or you wear glasses, is that the case in Brazil too? What if during an operation Matias breaks or loses his glasses? He will keep searching for the glasses and the enemy will shoot him.