I've owned both a Traveler and a Tiger and have a bunch of hours in each.
1) Some say they are "hot" airplanes, with high wing loading. They are not.
Comparable wing loadings:
AA-5B 17.1, Cessna 177B 14.4, Piper Archer 14.8, Beech Sundowner 16.7
AA-5A: 15.7, Cessna 172P 13.8, Piper Warrior 14.4, Beech Sport 14.7
AA-1B: 15.9, Cessna 152 10.4, Piper Tomahawk 13.4, Beech Skipper 12.9
So, the Grummans do have somewhat higher wing loading, but that's a significant part of why they are so much faster than their competitors, and also why they ride better in turbulence.
The 2-seat AA1 series did lean in that direction, and when used as a trainer without taking it's different flight characteristics into account, it could "bite" and was involved in more than an average amount of accidents. But this is NOT true of any if the AA5 series - nice, large, "Hershey Bar" wing with no unusual characteristics.
The original AA-1 did have a different wing, and has a few unique quirks which must be learned, but the later AA-1A/B/C have the same "cuffed" airfoil as the AA-5-series. The biggest problem we have with the AA-1A/B/C and AA-5-series is people trying to fly them too fast on final. OTOH, you cannot fly the original "slick wing" AA-1 the same way as you fly the other 2-seat trainers of its class (C-150/152, PA38 Tomahawk, and BE77 Skipper) or you will add to the disturbing statistics which led American Aviation to change the airfoil after the 1970 model year.
2) One can watch small airplanes land at small airports and see that lots of pilots land very "flat" - often 3-point (talking tricycle gear here). With damping on the nose gear, one can usually get away with that. But the Grummans have virtually no damping in the nose gear - it is primed to bounce back into the air if the pilot lands flat or even nosewheel first. This is NOT just an issue for Grummans - most Cirruses and Diamonds and Mooneys and the like have similar nose gear for the sake of simplicity. Just make a point of landing mains first and it should not be an issue. My Grummans both handled "full stall" landings just fine, and they were my SOP, conditions permitting.
...and after landing, hold the nosewheel off until you are almost out of aft yoke travel and then gently lower it to the runway.
3) Proper adjustment of nose gear friction is important. Too tight and ground operations are difficult. Too loose and shimmy will be a problem. A simple fish scale can tell you if you're in the right range, and adjustment is straightforward - though not listed as a owner maintenance item.
This isn't hard to do and is clearly described in the maintenance manual.
4) With the nose gear free castering, one must be careful not to drag the brakes. The key is to taxi in the Goldilocks Zone - not too fast and not too slow. Fast enough that the rudder is effective and not so fast you need a lot of brakes to keep the speed in check. Best to "stab" the brakes as needed for directional control rather than drag them. One can even use taxiway and runway "crown" to assist. Again, this is common to all deigns with free castering nose gear.
Agreed.