Quick self confession with a couple of stories to boot...
When I obtained my intial flight instructor certificate it was a long drawn out process. When I left the FSDO, I walked outside to the airplane I had rented for the test, and breathed a sigh of relief. I had just flown with an inspector, knew the airplane had fuel and a very thorough preflight and postflight. I jumped in, got my clearance, and took off.
I was coming from an ag background, and that's largely feel, very much eyes-outside-the-cockpit type of flying. I was about fifty feet in the air before I glanced at the ASI for a peek, and noticed it was zero. A quick glance at the pitot tube confirmed that the tennis ball I had placed over it during the postflight was faithfully in place. Amid the satisfaction of having completed the checkride for the new certificate was the humbling self-reminder that deep down inside, I'm really an idiot.
I had lots of runway ahead. But I was in the air. It was clear, VFR, and it was a light airplane that didn't really care if the ASI worked or not. I flew home and removed the tennis ball behind a hangar before parking back at the rental facility. Attempting to land on the remaining runway would have been risky vs. continuing with what I had. The real issue was that while this had just been a minor annoyance it could easily have been a real problem....then again, 61 passengers and nine crewmembers died on Aeroperu 603 in October of 1996 when workers washing the aircraft failed to remove tape from the static ports...little things become big things.
At the other end of the spectrum, a week ago I wasn't looking at the airspeed indicator as I pushed over a cliff into a narrow canyon. I was focusing on a burning tree half way down the cliff on the other side of the canyon. I retarded the power to idle and used a lot of left rudder and aileron, and forward stick to keep the target tree off the nose as I entered the drop. I felt a very violent shudder and then a buffet, and I would have sworn that the left wing was about to separate. A very loud rumbling and shaking occured, all the panels on the side of the fuselage began slamming, and the stick locked up. A red mist of retardant began swirling up from under the aircraft and the nose began coming up. The top of the wing got coated in retardant, as did the fuselage and cockpit, and I cleared the cliff on the other side of the canyon by a reasonably small margin.
I experienced a regime I hadn't been in with that airplane before; it as a high speed stall. It during the event, it loaded the retardant hopper enough that it forced the doors and dumped half the load. I never touched the trigger. It was very loud, very violent, and the stick was locked up with little effect from my input.
The point of that was the airspeed shot a lot higher than I had wanted it during the dive, but I wasn't watching it. I was watching my target, and once I cleared the ridge line to drop into the final run, the upslope wind that I'd felt on the run-in died, and I fell right out the bottom. My first clue, being oblivious to the wind noise and being far too focused on that tree, was sensing sinking into the canyon...all the rocks began rising in the windscreen instead of staying put, and when I did try to pull, the aircraft wouldn't recover. I flew out because the loading in the diving turn forced the retardant out by overpowering the tank doors...I had nothing to do with it.
The point, again, was watching airspeed can be pretty darn important, and failure to do so can be costly. Little things become big things. You probably weren't going to run into that much drama flying the 172 home, but you were right to take notice and handle it as you did. Noticing sooner would have been better, but you made a good decision to continue the takeoff when you did, and a good decision to come back and land.