Higgs mass

Okay, let me get this straight: if the Standard Model Higgs is only renormalizable for a particular choice of the Higgs' mass, this is not considered a prediction but a flaw of the model. However, if bosonic strings can only be made consistent in 26 dimensions, or superstrings in 11 dimensions and with the help of supersymmetry these thing for which there is zero empirical evidence are considered predictions of string theory and not flaws. Moreover, were a supersymmetric particle discovered, this would be considered evidence of string theory even though supersymmetry doesn't require string theory. You said it right, though:

the exact Higgs mass ... should be a free parameter in the standard model, otherwise we could stop searching in a range, and it is used by about every theorist who wants to endorse Susy, so it should be a real effect.

Since you're an experimentalist I hope you won't take the above personally, but anyway I'll offer you a bet that the Higgs will be found at 116 GeV.
Martin:

Unless the Higgs has pretty much exactly 116 GeV, so called loop corrections will destroy the model once more, if there are not more particles to shield these effect.

Dark Energy

As for Dark energy, I'm going to go with the Cosmological constant until there is any evidence to the contrary. As far as I know, even "exotic matter" can't produce a "negative pressure" stress-energy tensor.

Neutrino Mass

I don't consider throwing in a one (or several) right-handed neutrinos and a KCB mixing matrix a challenge to the Standard Model. "Explaining" the masses of the various particles is a challenge, but as far as I can tell there's no candidate for a theory that does that. [No, String Theory is not it: apart from having a proliferation of vacua, the only way they can get a low-energy spectrum of particles is by assuming they all have zero mass, nobody has a mechanism for supersymmetry breaking and the supersymmetry breaking scale just introduces a whole bunch of new parameters to explain.]

Dark Matter

My guess is as good as any other - but if dark matter only interacts gravitationally it won't be seen at the LHC. Actually, the quantum numbers match a "superheavy right-handed neutrino" too...

We have met the enemy, and he is us — Pogo