We seem to show a random episode here and there, but never the whole series, so here's some of the story of the first few episodes for you to get a better grip on what's going on. Like the opening says, labors became the primary workhorses of industry and construction (putting Caterpillar and John Deer out of business), and with this came a new type of crime. So a special vehicle division of the police was created to deal with it. The first unit is filled with skilled and highly-respected officers, and so naturally, Patlabor isn't about them. The second unit gets staffed by rejects and oddballs because Masami Yuuki likes to tell stories about weirdoes. So the TV/manga starts with the formation of SV2 and the addition of Noa Izumi to the crew. She's a puny transferee from the Motorcycle Division and a labor otaku. At first, they don't even have their labors yet, but they're being issued the brand new AV-98 Ingram model, fresh from Shinohara Heavy Industries (a top maker of labors). Then, an officer from NYPD joins them. Of course, she's Japanese-American (speaking a total of 4 languages) and will go back to NYC to begin a labor police unit there after she trains with SV2 for 6 months. Her name is Kanuka Clancy, and she has a PhD in EE from MIT.
They have a sort of contest to see who will be the pilots of the labors, who will be the "forwards", and who will be the carrier drivers. Noa and Kanuka win, but since Kanuka will go away, the third place Ohta Isao gets the piloting job. This is because the Ingram's OS learns with the pilot, and if the pilot changed, it would result in a sudden drop in effectiveness. Kanuka is Ohta's forward and Asuma Shinohara is Noa's forward. Shinohara turns out to be the son of the owner of the labor company of the same name. His intimate knowledge of labors comes in handy many times. The forwards are really the brains of the labors; they basically coach the pilots and act as extra eyes and resources and stuff. The carrier drivers, Hiromi Yamazaki and Mikiyasu Shinshi, are sideline characters. Hiromi is a large gentle man who likes to garden and raise chickens (sadly, two of his "pet" chickens are cooked in a hilarious episode involving a sewer chase with a large alligator). Shinshi, unlike all of the other SV2 members, is married (to a seemingly cute and sweet but very demanding/high maintenance young woman). Kanuka is later replaced by Takeo Kumagami, a very competent and "normal" officer with a phobia of most things supernatural. Most episodes deal with random cases assigned to SV2, and some cases they get involved in even though they shouldn't. There are some story arcs, the most notable are associated with the villains of the first OAV series -- the company Shaft and its head of R&D, Richard Wong. Basically, they're a rival labor manufacturer to SHI, but they don't really mind selling to criminals and foreign powers and terrorists and stuff (forgive me for not really telling it right because I want to save space). Anyway, they send various labors against the Ingrams, and SV2 has to prove how good they are. Most significant is the Griffin, which is the focus of the middle part of the TV series and makes a later comeback in the second OAV series. The Griffin is possibly da coolest one-man mecha in all of anime (certainly in terms of looks).
I should also tell you about the two head engineering dudes, "Old Man" Seiichuo Sakaki, an older life-long mechanical engineer, and the next guy down, Shigeo Shiba. There, I told you...
My second favorite character in the series is Unit 2's chief, Kiichi Goto. He's far too clever and resourceful to be with the heads of the police force, so they put him in charge of SV2 to get rid of him. A very internalized thinker, he rarely doesn't have the whole thing figured out before the episode is half over. He's been in love with the first unit's chief, Shinobu Nagumo, but she cannot forget her previous love, even though (spoiler!) he's the bad guy in the second movie. There's a great episode where the two of them are driving home in heavy rain. Because of the weather, they can't get back and are forced to spend the night in a love motel. This isn't the type of show where anything would happen; it's a great episode because of their interaction with the situation.
I have no idea what episode you might see tonight, but I'm sure it's good just the same, so enjoy! (I really ought to know, being as I'm on the scheduling committee...)