Particles can't really be two places at once. But since we're knocking things around with our light beam, we can't say for sure where it is now -- so we instead talk in terms of probabilities of where the electron is, rather than saying matter-of-factly where it is. This is what quantum mechanics does, it calculates probabilities that the electron is in a certain place, probability it was going a certain speed, etc.
As others have mentioned, you are missing a couple of fundamental points of the double-slit experiement.
1) The pattern observed has nothing to do with the photons being hard to measure (classically photons are sent through the slits),
The pattern produced is exactly the interference pattern expected if light were actually a wave. The peaks and troughs of the two waves cancel each other out which results in the dark bands. Dual peaks or dual troughs reinforce each other, resulting in bright bands.
2) If this was a result of electric field build up and the "detector knocking particles around a bit", then it should also happen for a single slit (it doesn't). It also should not occur for photons (electrically neutral), but it does.
3) "when single particles are allowed thru, we see only single points on the detector"
This is incorrect, and the weirdest thing about the experiment. If two slits are opened, and particles are sent through one at a time, there is still the same interference pattern created. Individual particles behave as if they do not have a fixed location, but only a probability of existing at a specific location.
Heisenberg's principle is a result of quantum mechanics and wave-particle duality, not the cause.