What tolerances should I use for spoke tension when building a wheel
This blog post (google cache, original gone) on the Park site suggests a range of 20%, this thread has people saying a range of 1 on the TM-1 is fine (edited in some quotes):

I sort of try to finish within a 0.1 mm error radially/laterally and under 0.5 notch (of the tension meter) of standard deviation for all spokes.
I get DS tension under 1 notch on the park tensionmeter.
Average: 14,25 (notches of the park tension meter) Standard deviation : 0,58 notch

That's what I generally use when building a wheel. I'll look up the chart and get something like 15.5 for a 1200N tension, so I'll aim to have all spokes between 15 and 16, and most of them close to 15.5. With a TM-1 I know my repeatability on measurements is only about +-.25 anyway, so if I measure the same spoke several times I'm likely to see 15.5, 15.75, 15.5, 16... and say &quot;buggrit, that's a bit over 15.5&quot;. But for any single measurement I could in theory chase the 15.5 target and go 1/4 turn looser or tighter, squeeze a few spokes then re-measure. But that wouldn't necessarily tell me I'd helped the situation, and might not even be accurate to within the tolerance I think I'm aiming for.
The actual process is pretty repetitive:

get the wheel fairly round, focusing more on up-down than left-right circularity (hops are hard to get out later)
run around and tightening spokes half a turn at a time to get the tension slightly under my target (say 14 using my 15-16 target)
get the wheel true to 0.5mm or so
Then I'll run the tensiometer over the whole wheel to see how even the tension is. If there's a big problem I'll back everything off a turn and try again. Otherwise I'll back off any over-tight spokes a little, tighten the loose ones and stress relieve the wheel, hoping it comes right. Then I'll re-true it. And repeat this step. Again and again, until it's all good.

Once you get the hang of it a lot of those steps will happen once at most. Normally I'll hit each spoke maybe twice with the tensiometer, and possibly a couple of spokes more than that. A good build would be tightening by feel, getting it true with a couple of tweaks, measuring and it's done. But that's very rare unless I'm on my third identical wheel in a day. If I'm fixing an existing wheel I might end up working 4-5 spokes 5 times or more trying to get it right.
One test I suggest you do is just to write down the tension of each spoke on your wheel, then put that bit of paper in a safe place. Then do it again, so you're measuring without looking at the earlier measurement. Then compare the two sets of measurements. That will give you an idea of the variability of your measurements of spoke tension. There's no point trying to get more accurate than that with a wheel, because you're chasing a random number.