My only real issue with Connery's performance in Last Crusade is that he doesn't seem to know how to play "clueless" convincingly. So when Dr. Jones Sr. was befuddled by the circumstances he found himself in, I didn't buy it for a moment.
I think Connery did a fine job as a fustian, bumbling professor and I had no problem buying the performance. I just didn't see how his cliche-ridden character could be Indy's father (and hated the idea of the writers trying to explain Indy in dollar-book Freudian terms in the first place). And they totally robbed Denholm Elliot's character of any dignity and made both him and Connery play silly old men, mainly for cheap laughs. For me Connery is the Jar Jar Binks of the Indy cycle.