What period we are speaking about? Travel between countries was generally heavily restricted until Krushchev's Thaw but since 1960's the rules were relaxed. Also, remember that in Warsaw Pact passports were a may-issue documents and came in two versions - one allowing travel to other Warsaw Pact countries, and one allowing travel to 'all countries of the world' i.e. outside the Warsaw Pact. Additionally, getting a passport, especially of the latter kind, was much harder in USSR than it was in satellite countries (as a rule of thumb it was easier to get into USSR than out). Until 1980's there was also a specific passport needed to travel to Yugoslavia that was not considered a 'Western country' but not exactly part of Eastern Bloc. Passports were short-issue documents, so you had to apply for one basically every time you were travelling abroad, so the trans-border traffic was closely monitored by authorities.

#1 - In most cases - yes. I haven't observed much differences between Czechoslovakian, Polish, Hungarian and Bulgarian checkpoints. As most functional buildings in an Eastern Block they were anonymous concrete blocks with a queue of cars and people waiting for their turn. Soviet and East German checkpoints had a more military flair, but they were not that different.

But there were some exceptions, of course. Checkpoints between East and West Germany were pretty heavily guarded with state-of the-art traffic disruption devices and the control was very thorough. The checkpoints between Romania and Hungary were even worse. Due to animosity between these two countries, fuelled by territorial conflict over parts of Transylvania and exacerbated by tyrannical Ceaucescu government, people entering Romania, especially Hungarians were thoroughly checked, sometimes interrogated in guards got suspicious for no reason, and having any materials that could have been considered 'subversive' (including foreign newspapers) could have been grounds for detainment. This particular border was pretty much 'Papers, Please' in real life, with even more hostile guards.

#2 - Not really, at least not when people were travelling with families (and they usually were). Inspectors were first checking your passports and there were virtually no problems here - if your document was genuine, you have nothing to fear. Customs inspection was the harder part, but again, if you were transporting nothing of importance, this was a general glance in the trunk and inside of the car. On East-West Germany border, one-on-one talks, often recorded, were much more common (well, it wasn't called 'the most closely guarded border in Europe' without the reason).

The socialist economies were centrally controlled, so the prices for similar things could vary greatly and some common things were simply banned (oral contraceptives in Hungary, condoms in Romania), so when the regulations of travel were relaxed, people often treated the trips abroad as a means to eke out usually quite meagre salary with some trade or even barter. So it was not uncommon to return from a trip to Black Sea resort with say, a new TV, half a pound of gold jewellery, silver cutlery set for 24 people and a bulk box of aspirin (having sold several drills and three transistor radios that happened to be cheaper in your country). In such case, inspectors were more picky. Of course, everyone knew what's going on, but technically no one was breaking the law - you could travel with whatever you wanted. Confiscations were not that common, bribes (more often than not, some item carried for sale abroad) were much more common. In some places they were almost expected and many people were calculating them into the travel expenses.

If the guards were bored or suspicious, they could check the car or baggage thoroughly, to look for foreign currency, drugs or other illicit items (Cold War was very real back then), but this was rare and usually happened at the airfields and checkpoints leading outside the Eastern Bloc. Paradoxically, the common procedures were less strict than modern ones - no metal detectors, no personal checks, no x-ray checks of luggage etc.

As a side note - Westerners were scrutinized much less thoroughly (on a safe assumption that they were not coming here to trade), in USSR or East Germany their luggage was usually checked just to make sure they are not smuggling anything espionage-related. In turn, they tended to be closely monitored in their place of arrival, but this is another story.

#3 - Mistakes in paperwork were very rare, much like today. Basically, all the 'paperwork' was done in your country before you got a passport. If there was something unclear, or missing, the citizen had to correct the mistake or his request was simply rejected on the grounds of incomplete paperwork. On the border, you just had to show your passport and sometimes also your citizen ID. When being issued with a passport, you were (and still are) obliged to check whether all data is in order, because officials are people too, and clerical errors happen. All the inspectors checked was whether the personal data match and whether the passport is valid and allows you to enter this particular country.

#4 - Not really. As I said, the passports were issued arbitrally, so the main problem was getting them in the first place. During important political upheavals (Hungarian revolt in 1956, Czechoslovak uprising of 1968 or martial law and rise of the Solidarity in Poland in the early 1980's etc.) officials were simply rejecting the requests for passports to or from a particular country.

#5 - Well, it depends. USSR and East Germany border guards were considered the least prone to everyday corruption mainly because these borders were considered of utmost strategic importance and thus the work of the guards was closely monitored (taking a bribe could easily be construed as compromising national security). Guards on the other borders, as I said before, often were taking bribes from people ostensibly stretching the rules (selling personal items abroad was not strictly legal, but simply moving them across border was).