So I've taken 2 private, half-hour lessons with a guitar teacher, and I'm not sure how to figure out if he's a good teacher or not. So far he's taught me a simple song, and then moved on to strum-patterns and a few chords.

One thing I noticed is that he hasn't really critiqued me much on my playing mechanics. For instance, he hasn't really observed how I hold the pick (beyond just telling me how to do it the first time), hasn't told me if my right-hand strumming/picking is correct (if my hand position is right, if my motion is correct, etc).

I've only taken 2 lessons so far, but I'm assuming these should be things that he's actively critiquing me on tfrom the start o make sure I don't develop any bad habits? Is this a sign that he isn't a good teacher?
Maybe he's letting you get through the first couple of lessons easy so he makes sure you keep comming back, and dont get put off by a strict teacher, I bet as you start progressing farther into your lessons he'll start getting more strict about those minute details, as they are not as important as you first start out.
But I (If I was a teacher...I'm not good enough to be, or old enough) would start picking on those little details, but It just goes with other peoples teaching styles too
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Most teachers will be easier on you for your first couple lessons or so just to see where you're at. It sounds like he's doing the same. He'll probably move on to different things later.

Hard to tell with only 2 lessons, but he should be checking out what you are doing and making sure you are doing it properly. One thing you should do is remember to "hold the neck like a hamburger." make sure your thumb is in the middle of the neck (right in the center of the arch) because that has a lot to do with conservation of motion. Be sure he's not just ripping you off. If he starts trying to teach you stuff like Mary had a Little Lamb and Hot Cross Buns and sticks to that for way too long then he is surely ripping you off. You should start out by learning your 5 basic chords. CAGED. Learn to form those chords with you index, middle, and ring finger and then learn to form those chords using your middle, ring, and pinky fingers. The reason you do that is because all chords (well almost all) use the same "chord shape/form." Then by the time you are ready to learn bar chords it shouldn't be too much of a problem for you. If you want any beginner advice then just PM me with any questions and I will happily answer them for you.
I think my teacher is good, mainly becuase he's taught me in the lessons I've had, the basics. It's one thing having a book and reading it, but you can't ask questions which is why a teacher is so good to have. If i'm unsure about how i'm doing, atleast I can ask, and he can show me what i'm doing wrong. I started learning basic stuff, like how to hold the pick, and stop buzzing sounds - you know when you're holding the pick right when you don't get a buzz from the string, how to hold the guitar and where to put your fingers on the fret, the first few weeks before my first lesson I was playing tunes with my fingers actually on the frets, I was trying to-do tabs and when I had to hold my fingers on the same fret and doing the occasional harmonic, it was impossible - but having a teacher correcting me, has made appreciate having lessons - it's made me sound better already, becuase you think he may laugh at you, but it's like anything - You have to learn silly things, be embarrsed - just makes it more fun, and having a teacher help you reach goals.. like learning a intro, gives you an incentive to progress when you feel dis-couraged or unsure of what to move onto next. The problem you may find, or what I'm having - Is sometimes he'll give you something and you'll pick it up really easy, and then the next week you'll have something really hard - so some weeks your struggling and just wanting the days to go past so you get your next lesson, and others your fearing the next becuase you've not learned what you were supposed to. I guess we all move at different paces, but it sounds like your teacher is cool like mine, good luck!
I think the best way to decide if he's a good teacher is ask yourself, "Am I learning anything?"

If you guys are just jamming then I'd say no but if he's showing you stuff that you don't already know or is helping you with stuff then he's probably decent.

It is hard to tell after two lessons though.
Thanks guys, those are all good points. I'll take a few more lessons before I decide. I definitely feel like I'm learning though, which is good. I just worry about developing bad habits, or not practicing optimally.