For your second point, H-H is weaker than O=O because of the double bond I would have thought. Even so, O=O isn't much stronger than H-H according to some sites I see on the internet. O-O, for instance, is VERY weak.
What other factors would there be? There would be influence due to surrounding atoms, but VCE wouldn't consider that.
Is atomic mass really more significant? From my limited physics knowledge, the frequency of a spring's vibration depends on the inverse of the square root of the mass.
To be fair, I'm not sure how to estimate the force and its dependency on distance, but I'm sure it would be more than inverse square root of distance. I mean, http://www.cem.msu.edu/~reusch/OrgPage/bndenrgy.htm says that F-F is stronger than O-O, which supports the fact that distance does play a part in determining bond strengths. What else is there? I'm curious.
In the context of vibrational frequencies, the bond strengths just get lumped to together in a constant, k, called the "force constant" (analogous to the stiffness of a spring), so any distinction between discrete single vs. double bonds get lost, which is why I considered H-H vs. O=O to be a fair comparison. Moreover, the distinction between discrete single and double bonds doesn't really work anymore once you start doing molecular orbital (MO) analysis.
Now, to be clear, I never meant to say that atomic radius wasn't a factor at all! I was just trying to argue against the idea that it's as equally good an explanation in the context of that question as atomic mass. Atomic radius certainly does play a role in bond strength. However, don't forget that it's bond 
strengths which have the direct affect on the frequency of vibration. Now, a C-H bond has a bond energy of around 98 kcal/mol whereas the C-O bond in methanol has a bond energy of around 91 kcal/mol (unless Wikipedia is lying to me). These values aren't massively different, suggesting that the bond strengths also aren't that different. In contrast, an oxygen atom is 16 times more massive than a hydrogen atom. As such, bond strength (and hence atomic radius) isn't going to be the biggest influence on vibrational frequency here - atomic mass is.
The other sorts of considerations I was thinking of arise when you start doing MO theory; you have to consider things like orbital overlap and symmetry (i.e. lots of scary integrals and algebra). That said, when I think about it, I suppose that's really just the MO equivalent of thinking about atomic radius... Other than that, electronegativity difference and EDG/EWG substituent stuff are a very important factors, but you've already talked about that.
As an aside, be careful with talking about "bond length/distance" as a factor (as opposed to atomic radius) because, in my opinion, it's difficult to establish the line of causality clearly (is the bond short because the atoms are tightly bound together or are they tightly bound together because the bond is short?).
PS: Sorry for us semi-hijacking your thread, stankovic!