The cylinder that Reese takes that is marked Liquid Nitrogen is a standard gas cylinder incapable of storing the supercold liquid. When he sprays the computers, he is not wearing any protective gear. If this were liquid nitrogen, he would have severe frostbite. The 'snow' when he sprays the computers indicates the cylinder probably contains carbon dioxide and the 'snow' is dry ice.
When Harold and Root are utilizing the PS3 consoles, they begin to overheat, overclock and melt. However that is not a failure mode for these computers. They will downclock to protect themselves, reducing performance but no permanent damage occurs.
It is impossible to shoot through such a steel chain with a handgun. This has been empirically proven many times over.
When Harold is trying to decompress the machine, he says "there's not enough room", "there's not enough memory". Later, when Root and John are helping, Harold says "we don't have enough processing power to decompress the machine. " When decompressing a large image, processing power is never the issue as long as there is not a time constraint. Memory and storage are. Running the program after decompression has completed is another matter.
B.S.O.D. (Blue Screen of Death) is a Windows phenomenon. Neither of the AI servers would be using Windows, most likely it would be a heavily-customized Linux or Unix. The Linux/Unix equivalent of BSOD is a kernel panic.
After the shootout toward the end, Reese says they need to leave because they're "low on ammo." But there are four heavily armed dead guys lying on the ground right in front of them. They could just grab their guns.
Throughout the first half, Finch says that they are running out of time when the light turns red on the briefcase, that if the light starts blinking, they'd be in big trouble, and when the light goes out, he says that there is a small amount of residual power remaining, that it is probably losing data, and yet he has time to putter around, to stop trying to open the briefcase to listen to Fusco's phone call (17:35), to try to convince John not to go find Root (22:35), and even for a brief soliloquy.
Leaving a voicemail, Fusco's term "nuclear fustercluck" is redubbed "nuclear fakakta" by order of the network. The original line survived in the promo.