I'm not in the sciences, so I can't speak to actual things you might want to do in the lab, but here are some general ideas.
1. Think of yourself as an apprentice, not as a professor.
I took a TAship this year instead of a teaching position, because I wanted to devote myself as fully as possible to my dissertation. I've been TAing for... holy crap... nine years. I've been at this for a while, and have also taught a bit on my own, and so the profs I assist tend to give me a lot of leeway. But still, it's just a TAship. This is someone else's class. Not mine. My job is to help them carry out their vision.
And you know what? I've been really, really lucky. The professor I'm TAing for this year is amazing, and I have learned a lot of things that I can't wait to implement in my own classroom. If I had gone into this thinking that I knew what was best, either in terms of content or pedagogy, chances are the prof and I would have been at odds. (And in fact, this happened once. Only once, though. The prof was teaching something that I didn't agree with, and I actually (I still can't believe I did this) spoke up in class about it. That will
never happen again. Never). My point is that, although I have very strong ideas about what is and is not effective in the classroom, I made a conscious decision to go into this position with an attitude of apprenticeship, and it has made all the difference.
Also, this prof makes a lot of "extracurricular" requests of his TAs. (No, Spork, not those kinds of requests). He wants his TAs to go to the library for him, to take care of his administrative tasks, to make photocopies for other courses he's teaching, or do grunt work for a conference he's organizing, etc. A lot of his TAs balk at this. They say things like, "That's not what I'm paid for! I'm not an errand person!" And they're right, of course. But because I'd adopted an attitude of apprenticeship, when Prof. Big Name would ask me for these favours, I'd do them. Hell, I was going to the library anyway. It would only take five minutes. And you know, Prof. Big Name has become one of my stronger supports in the department. He's written me wonderful letters of recommendation. He's gotten me additional funding. He's agreed to read over parts of my dissertation that fall within his specialization.
That attitude of apprenticeship will not only save your sanity, but might just yield some unexpected fruit.
2. In a similar vein, remember that you don't know what all you don't know.
For instance, you're assuming that a first year intro course should both introduce students to the discipline and spark interest in doing a major in the discipline. Some intro courses are designed that way (that's the norm in my discipline). But others are designed to weed out students. Sociology and Psychology intro courses were weeders at my undergrad institution. The honours programs in those disciplines were rigorous, and they only wanted the best, so they weeded them out early.
Maybe your department does this. Or maybe the department doesn't, but the prof you're TAing for thinks that they should. Or maybe the department intends to introduce a specialization around that particular prof's expertise, and is changing the structure/content of the intros to reflect that. Or maybe the department isn't doing it, but the prof wants that to happen, so is including more of his specialized research into the intro course in the hopes that more students will agitate for courses in that area.
In the end, though, who knows what's going on? The point is, you don't. And even if you did, it wouldn't be your place to change it. You're not the professor. You're the minion, carrying out someone else's vision.
It's also possible that there are aspects of the field that you don't know about. After all, this is why you're a student, right? Maybe this narrow field of research is actually important in ways that you don't realize. Or, maybe not. But you're not really in any position to make a definitive judgment.
3. Correct errors in class.
This is not a big deal. The manual is wrong in places. Oh, well. You'll catch it before class or in class. And you'll correct it. The end. As long as you tell the professor which details you've corrected (so students aren't marked wrong on those details), I don't see the problem.
It is rather with having to use materials that ought to be authoritative that contain errors both in fact and reasoning (always accepted by co-ord when caught, who tells us we'll just have to explain to our students that the manual is wrong).
This is not my fault, but it reflects badly on me as the person presenting the information.
No, it doesn't. Well, it would reflect poorly on you if you were presenting the wrong information. But you're not. You're correcting the manual. This is no big deal, and it seems like the professor recognizes it as such. It sounds to me like you think that the fact that he treats it as no big deal indicates a lack on his part - a lack of caring, of understanding, etc. I think it indicates his experience. You could learn from this.
It's also really hard to summon enthusiasm when I know I'm teaching very little of general importance every week. My students don't explicitly know this, but they probably pick up on it to some extent, unfortunately.
This is your cross to bear. If you want to be gutting fish instead of TAing, by all means, free up the spot for someone who wants it.
How can I effectively teach material I don't really give a crap about, and for which I cannot forsee any possible use for my students unless they join [specialist field]? I can manage teaching areas where either one of those is false, but not both.
See #2 above: You don't know what all you don't know.
Teaching and grading already takes up most of my time and I have my own degree to worry about, so spending much more time on it is completely out of the question. While I enjoyed teaching stuff I could see the point of last semester, this semester I am becoming resentful of the time I'm spending on teaching because it's a) a time drain on my part and b) a waste of time for my students as far as I can make out.
I say this with tenderness: you're whining. Cut it out. Let me channel my father for a moment: "Grassy, that's why they call it work and not happy fun play-time!"
Okay, those are all goals. I know I have to live with the system for the next year and a half, and I shall do the best I can while I must.
Caught up in circles, confusion is nothing new. Didn't you just begin a doctoral program? How come for only a year and a half?