We ran two playtest that included a swashbuckler... one at 4th level, one at 7th level. At 4th level, the swashbuckler was a bit mediocre. Some of that was because we had an entire party of hard-hitting melee characters, so the swashbuckler's panache was quickly used up and all the other hitters made it hard to get a killing blow in. At 7th level the swashbuckler was really great... he was critting all over the place and easily replenished his panache.
We haven't played one up from 1st level, so haven't had direct experience with the pain of no finesse until 2nd, but I can see that it would be annoying. However, I understand the wish to avoid easy dips, and it's not much different from the pain non-human or non-fighter archers have to go through waiting for precise shot, or the pain of a 1st-level wizard who is instantly out of spells. I think the class is still quite workable even if finesse is kept at 2nd. I did like one person's suggestion of giving the swashbuckler combat expertise... the flavor of the class is well-suited for fancy trip/disarm maneuvers, but with the need for charisma it really can't afford a 13 Int. It would be nice for the class to get the feat as a bonus somewhere along the line... or perhaps be able to qualify for the feat using charisma instead of intelligence.
I didn't see any problem with the weapon limitation... but then, we like rapiers. I also didn't see any need to change the precise strike (other than to make it effective on anything that can be critted). The 7th level version was doing PLENTY of damage! Not as much as a raging/power-attacking/two-handed weapon Barbarian... but that's not the role I see for this class. When I was first looking at the class, I was mentally comparing it to a rogue rather than to a fighter. It has the rogue's light armor, restricted weapons, and emphasis on skills... but gets full BAB and d10hp, and doesn't have to get into flank to get its extra damage. It loses the trap finding... but isn't squishy. We quite enjoyed it.
Someone also brought up the relative scarcity of trapfinding. This is true... but you can always take the trait that makes disable device a class skill, and train up your wizard or witch or arcanist with it. Their int bonus goes a long ways towards compensating for the lack of level bonus. And of course alchemists can also do that without the need for the trait. Despite my comparison of swashbuckler to rogue, I don't think the swashbuckler needs trapfinding added to it.