If/when you get another flat, don't take the tube all the way out of the tire. Leave the stem in. Inflate the tube (yes, as it hangs outside the tire) so that you can begin to hear/feel the air escaping from the hole. Find the hole. Line the tube up with the tire, making sure to account for the curvature of the tire to find exactly where--on the tire-- the hole is coming from.
Check that spot on the tire meticulously. Also check the rim tape. If it doesn't completely cover the spoke holes in the rim, that could also be a cause. If the rim strip is narrow, and barely covers the spoke holes, get to a LBS and pick up some wider tape. It's cheap.
Also, make sure when installing a new tube to not twist the tube inside the tire. That way, if the hole is on the inside of the tube, you know it had to do with a spoke hole or a pinch flat. If it's on the outside, it came from a puncture.