The only flaws that really bug me are anachronisms in period pieces. There's no excuse for those.
For instance, in GLADIATOR, one of the Romans was wearing Reeboks.
How about the Tarzan movie where one of the natives was wearing a watch?

I personally don't really look for "goofs", but I do notice the cars and their years in period films, such as the '65 Chevy being used in 1963 in "Goodfellas".
Speaking of cars being used in films, Turnbull has made a post in the past detailing most of the cars used in the Godfather films and how accurate they were, even to the point of saying what type of brand would have been used by who.

What I found interesting is that Michael didn't always choose the typical "Black Cadillac" as his car of choice. Other then the scene in hotel room with Kay, where they showed a Black Cadillac parked outside the Hotel Washington,
and his return when he went to meet Kay
It appears that once Mike took over sole proprietorship of the family, he didn't use Cadillacs anymore.
Mike was shown, first in the Packard limo,
*Packard can be seen behind the Buick. I believe that Buick's were also favored by mob types on low end of the ladder.
then in Tahoe in the Imperial Ghia.
Also I believe Mike arrived in Las Vegas in a Chrysler limo
