I don't think I can drop $50-$100 for a torque wrench right now. What parts of a bike are the most critical to get the torque just right? Is there a way to make sure the torque is ok without a torque wrench? I know what would happen if you don't tighten enough. Too tight is probably better than not tight enough! Is there a way to make minor adjustments based on some sort of observation or feel?
You can't approximate torque by feel. Loctite, grease, carbon compounds can all alter the 'feel' when you are tightening down bolts and if there was anyway to 'approximate the feel' these variables render it fairly impossible.
If you use ti/aluminum bolts, carbon components, high end aluminum do not cheap out, get the torque wrench.
If you tend towards stainless/steel bolts and less expensive components, you can forgo the torque wrench and just ensure you are working to even torque. For example, if it is a faceplate make sure that the gap between faceplate and stem is even all the way around.
Saying 'too tight is better than not enough' is not true. Too tight can create stress risers in a component (specifically I am thinking handlebar) that can lead to catastrophic failure down the road. Too tight on a square taper crankset (specifically the fixing bolt) can cause deformation of the taper fit and eventual loosening of the crank.
Hopefully that helps.
Noticed I didn't answer the question fully.
Faceplate/Bar interface Stem/Steer interface Crankset (whether pinchbolt or square taper style BB)
Those are areas where I would ensure proper torque. Seatpost is dependent on style of bike (ie. Madone seatMAST, or carbon post/carbon frame) as to whether torque is super important. Rotor bolts, brake mounting bolts etc... but with increasing importance as exotic materials increase.
In my area, Community Cycles is a non-profit organization promoting bike riding. For a modest membership fee (less than the price of a torque wrench) one gets access to their bike shop's tools. Their site includes a list of other bike collectives in North America, which might be a good alternative to buying your own tools each time you need a new one.
Too tight and something will break, it may be the thread on the bolt, or much worse the thread on in the hole. Bolts will also break, sometimes leaving a very hard to remove bit in your frame.
Not tightenough and it will work loose, and then you know to do it a bit tighter next time.
(You don’t need to be spot on with torque, just not a long way over or under)
However wheels and brakes are not hard to do without a torque wrench, so a lot comes down to what maintenance you will be doing and how much your bike is worth.