It is probably worth noting that while Khrushchev was initially more 'liberal' on certain topics, he still had certain lines that people were not allowed to cross. For example after the criticism of Stalin in his Secret Speech, the basic contents of it were to be discussed at local party meetings. When some party members took this as an opportunity to point at the fundamental issues with the party (instead of how bad it had been under Stalin, and by association how it was supposed to be better now), many were sanctioned for it. The party centre issued further instructions effectively outlining what was 'allowed' and what what wasn't in future discussions of this sort. Similarly, depending on what you consider a political crime in the USSR, Khrushchev was always quite harsh when it came to speculators - this covered an assortment of economic crimes but tl;dr involved reselling items on the grey/black market.

Similarly later on in his career Khrushchev started to turn on artists and dissidents who he thought had gone too far. IIRC in 1962 Khrushchev attended one art exhibit and criticised the works he saw and made some fairly derogatory remarks to the artists involved. While literature about the Gulags etc. had been published early in the piece, later on authors found it increasingly difficult to publish on such taboo topics, or were being pressured to edit out certain sections.

So into the Brezhnev era there was a continued swing towards conservativism and a bit of a 'rehabilitation' of Stalin. The iconic moment which highlighted the turn against artistic dissent was the Sinyavsky-Daniel trial, which targeted two writers who had published writings that were seen as critical of the USSR in foreign countries, and both received a heavy sentence (Yuli Daniel got five years hard labour, Sinyavsky seven years).

Another semi-new* feature of repression of political dissidents in the USSR was the use of psychiatric detention at Psikhushka. Political dissidents instead of going to trial were being found to have "sluggish schizophrenia", with their stated protests etc. against state persecution being portrayed as signs of dillusion and illness. So dissidents were often placed in psychiatric hospitals instead, where the treatment was often brutal. Pyotr Grigorenko, who had previously held a high rank in the Soviet military was one example of someone who was detained this way after his protests against the invasion of Czechoslovakia.

On the other hand it is worth keeping in mind this wasn't a full swing back to the terror of the Stalin era. For example under Brezhnev the most common intervention against dissident activity wasn't arrest, but having the involved parties report to the local KGB headquarters for a 'prophylactic chat'. Basically the KGB would tell the suspect their secret was out, warning them off and make some tacit/explicit threats of arrest and loss of employment etc. if they didn't straighten up. While this is still an oppressive tactic, compared to arrest and hard labour/'psychiatric treatment' it was relatively mild. Another factor reported is that while many things under Brezhnev were prohibited or frowned upon, there wasn't always strict enforcement. For example there were reports of bootleg music being sold in public places, often with the knowledge of local police. This somewhat lax enforcement at the local level goes some way to answering your question about what the regular citizenry would have noticed, but equally they would have noticed that reports about Stalinist repression had disappeared from the media, and some items could only be obtained as samizdat.

In some respects this varied enforcement probably reflects a bit of a shift in the type of dissent suppressed under Brezhnev - acts with a potential international audience tended to get a harsher punishment than something that was relatively private and benign.

Some references:

• Protest, Reform and Repression in Khrushchev's Soviet Union by Robert Hornsby

• Everything Was Forever Until it was No More by Alexei Yurchak

• Brezhnev Reconsidered, editted by Bacon and Sandle

*I say semi-new because punitive psychiatry wasn't invented in the Brezhnev era, but it became more systemic and common during that period.