Nothing, provided the hero starts out as a 35-year old and stays that way.

If you let your teen heroes grow into a 35-year olds, it follows that eventually you should end up with 80 year olds.

   It's gotta be the Hollywood mentality.  Old age is just SO OLD.  Nobody is a 30-something any more.

   I remember cringing a little inside when Peter Jackson decided that Frodo Baggins and his companions had to be Tweeners.  When JRR Tolkein wrote those books, Mr Frodo and Sam were bloody adults, dammit!

   Ah, the Fall is going to be so hard on those kids...

I know that as a kid the great appeal of Marvel Comics Group was in the way that the stories went beyond one issue and propagated across the Marvel Universe with plot lines developing on multiple levels.  But I think that this does impose some aging process on the characters which should have been better anticipated and planned for by the company heads some 30 years or so ago.  It's probably too late now.

We start with Reed Richards and Susan Storm not yet married.  We're informed in one of the issues that Reed and Benjamin Grimm served in WWII.  That by itself means that they were at least 18 in 1945, hence 34 in 1961 when the FF began.  Eventually  Reed and Sue marry and Sue becomes pregnant and eventually gives birth.  You can count that as 9 months right there.  Then we see that Franklin Richards does eventually grow old enough to be dressed in kid clothes by his governess Agatha Harkness and to say things like "Goodbye Mommy."  That must constitute a few years there.

Let's also not forget that the time-frame in which Peter Parker finished up high school was fairly close to ordinary calendar time, whereas his time in college was greatly stretched.  You can't say that he was just graduated from high school early for his age because of his brilliance, since all the others like Flash Thompson and Liz Allen also finished it around the same time.  Didn't Flash do a run of military service in Vietnam?  That would have to account for at least 6 months at a minimum.

While it is to be expected that the time-scale will be bent and twisted around in comic books, I thought as a kid that part of the appeal of Marvel was an odd sense that time was sort of moving forward with the characters.  The only way that I can think of that one might resolve such a conundrum is by a planned phasing out, retiring down and killing off of old characters and the introduction of new ones.  To be effective, something like that would probably need to have been initiated from the top management with a gradual shift being enacted over 30 years or so.

...a 35 year old Super Hero?

Considering Dick Grayson is now in his twenties, Superman and Batman are more likely pushing 40. Ditto for guys like Captain America and Iron Man with respect to Peter Parker.

Viet Nam vet Frank Castle is in great shape for a guy closing in on his 60s.