I like "The Last Crusade", too. I've liked it since the first time I saw it. I never took it too seriously, and I appreciated the comic relief from Brody and Sallah.
As for Connery? I think he played it well enough. How do you possibly play the father of Indiana Jones? And he showed that the way to do that was to depict him as smart, passionate about his work, and an absolute ballbuster with his son whose methods he finds questionable. I think that having him be afraid of rats the way Indy was afraid of snakes was a little ham-handed, but at least it wasn't overdone.
I think that movie and the other Indy movies are a product of their times, along with the nostalgia that Lucas and Spielberg had for saturday matinee serials and the 1930's. But does that 1980's meets 1930's sensibility work in the 21st century? Obviously something was not working when KotCS came out. Was it the story? Or is this a type of film whose time has passed?