Cole, the general "look" of Indiana Jones is basically the same in every movie. However, many of the little details change repeatedly from film to film, and that's what a lot of fans get interested about.
Stuff like:
How is Indy's hat bashed (that is, shaped)? What shape was the hat block used to put the dents in it? (It changed between Raiders and Temple.)
How is the jacket constructed? Does it have snaps on the storm flap? (No in Raiders and Temple, yes in Crusade and Skull.) Are the pockets large or small? (Again, it varies.) What about the shape of the buckles on the rear straps? (D-rings or square sliders? Once again, it changes from movie to movie.)
What's the construction of his holster? (It was a custom job in Raiders, vintage army surplus in the other movies.) How is his leather whip-holder strap attached to his belt? (Bolted on in Raiders, removable in the other films.) His satchel? (Its leather strap's color and buckle type vary.)
(Forgive me if I'm mistaking any of the details--this was written in a hurry!)
It's not your fault that you haven't noticed these variations. The filmmakers really didn't intend that you should notice them, and in fact, most people don't. But obsessive Indy diehards do see the differences, and once you know what to look for, they're as plain as day.
Now, as to the question of the beard:
I might have liked, hypothetically, to see Indy in a beard, as long as it was "Mystery of the Blues" length, and not that shaggy woolly monster Harrison sported in The Fugitive. Although I would prefer that Indy cut his hair a little down from the unruly MotB-length.
But I don't think Indy is the type to really sport a beard as his preference. As I understand it, beards weren't very fashionable in the 1930's. Certainly, they were not in any way stylish, and hadn't been since the onset of World War I. By the time of Raiders they were primarily associated with older men.
I don't imagine Indy would realistically be sporting the look of an earlier generation than his own. Indeed, as far as my own preferences go, I'd personally want him to be as fashionably modish in up-to-date 1930's styles as possible. (Though I don't mind if he keeps his 30's style up through the 50's, as really, it never grows old.)
A beard undoubtedly would have increased the resemblance between father and son. However, though I like the idea of a certain continuity in Jones family fashion style, I also think Indy should have his own "look," appropriate to the era he inhabits and embodies.
A mustache, on the other hand, is another story...
