Hulk, while a tough cookie, isn't shown to be as unstoppable as he normally is. While it can be argued that this makes his conflicts more interesting, it's interesting to note that this is explained in story. Banner has been working on a cure while in South America, and recent testing revealed that the gamma within him is much lower, possibly explaining the Hulk's limited strength.
In Captain America: The First Avenger, it's revealed that the super soldier serum strenghtens the user's main personality trait. In that movie, Steve Rogers is a selfless Determinator accustomed to taking a beating and keeping his cool, so as Captain America his heroism was increased; while Johann Schmidt was an evil and ambitious Mad Scientist, so as Red Skull his evilness was increased. In this movie, Blonsky lives to fight, so after taking the serum his willingness to fight slowly turns into full on Blood Knight tendencies, combined with Drunk on the Dark Side. As a plus, Schmidt and Blonsky both received an incomplete serum. Steve is the only one to get the formula as it was meant to be given (refined, in a lab, with someone who can handle it) which is why he is the only one that doesn't suffer horrific side effects.
Captain America is a successful Supersoldier whose main weapon is a gleaming shield because he'd rather defend the innocent than punish the guility. The Hulk is a failed super soldier who breaks cars apart to make crude shields out of self-defense. Hero+Super Serum=shield user.
In deleted scenes, Bruce is seen jogging across the mountains near the favela, and then through the favela itself. He was likely working on keeping his heart rate under control while exerting himself, as well as building speed and endurance, for the very purpose of being able to run away from the military if he had to without hulking out. He likely scoped out escape routes ahead of time in every direction, with traps like the gap between buildings which the soldier fell through because he couldn't see Bruce at the moment he jumped it.
When Bruce cuts his thumb at the bottling plant, you can see the blood, as it spins in mid-air, separating into two droplets. One half-drop lands on the brim of a bottle, the other falls between the bottles to land on the track below. Bruce couldn't see that happen, so when he found the perfectly round droplet on the conveyor belt below where he'd cut his thumb, he didn't realize that another droplet had already moved a good ways down the track while he was running down to where he saw the blood heading.
Some people complain it was too much of a coincidence that Bruce happened to be able to escape through his co-worker's window when climbing down from his own place. However, when Bruce first arrived in the favela and got the job at the plant, he likely needed a place to stay. It seems likely that either the factory helped him find a place, in which case they may have helped her find a place too, or that the co-worker knew a place right near her was open and suggested it to him. If the first case, it would explain why he ran into the factory bully, too, as all the factory workers were likely housed in the same area.
The tranq darts used in the favela were likely calibrated to Banner's weight, possibly even stronger than would typically be used for someone his size if they had past experience with him shaking off sedatives/anesthetics quickly. So while Blonsky shooting Bruce's dog with a tranq at first seems like a more minor cruelty, the poor pup, being much smaller than Bruce, would have received a massive overdose, almost certainly a fatal one, especially if he didn't get any medical care, something the military is unlikely to bother with and the favela is unlikely to have even if someone wanted to help.