This is a question about the self-consistency of the Standard Model - which I believe is the same as asking whether it is UV complete - in other words, can it be used to predict experimental results at arbitrarily high (and low) energy scales? Note I am asking for a rigorously defensible statement about the Standard Model, not a technical explanation of why said statement is true.
(An aside - I understand that the term "Standard Model" can include the original version (massless neutrinos), or various extensions that allow massive neutrinos.)
I understand that the Standard Model is certainly not correct at the Planck mass, and is not able to explain cosmological observations, so it is observationally falsified, but my question relates to internal self-consistency.
This note by Rubakov gives an attempted answer,
Standard Model is a well-defined theory, in the sense that everything is calculable, at least in principle, within this theory in terms of finite number of parameters (some quantities are hard and even impossible to calculate in practice because of strong coupling in the low-energy QCD). With $m_H \lesssim200 GeV$ this theory can be extended up to Planck energies.
In fact the Higgs mass $m_H$ is indeed less than 200 GeV.
The Wikipedia article equivocates:
The Standard Model is renormalizable and mathematically self-consistent(1)
(1) In fact, there are mathematical issues regarding quantum field theories still under debate (see e.g. Landau pole), but the predictions extracted from the Standard Model by current methods are all self-consistent. For a further discussion see e.g. R. Mann, chapter 25.
What is the best current answer?
Answer
The Standard Model is consistent in perturbative expansions.
It is inconsistent non-perturbatively but all these inconsistencies only show up "qualitatively" at energies well above the Planck energy – where we know the non-gravitational Standard Model to be inapplicable, anyway.
The inconsistencies of the Standard Model involve the Landau poles – the $U(1)_Y$ hypercharge coupling $g$ diverges at a certain energy scale, due to the renormalization group running – and a similar problem with the quartic Higgs self-coupling (it would be a problem at low, below-Planckian energies if the Higgs mass were higher than those 200 GeV).
A perhaps more serious problem related to the latter is the instability of the Higgs vacuum. The minimum at $v=246\text{ GeV}$ in the Standard Model isn't really a global minimum for certain values of the Higgs mass $m_H$. The observed $m_H$ is lower than 130 GeV or so and for these values, the potential isn't stable. It has lower minima at vevs $h\gg 246\text{ GeV}$. To say the least, the Standard Model potential is metastable (lower global minima exist but one can get there only through a tunneling which occurs rarely) with a dangerously short lifetime. Whether the metastability (intermediate situation) is an inconsistency – when all cosmological considerations are taken into account – is debatable.
But if one is satisfied with predictions at energies lower than the Planck scale and up to the accuracy of relative corrections of order $E/m_{Pl}$, then the Standard Model may pretty much be put on lattice and the continuum limit will agree with the perturbative expansions and produce a consistent theory for all these phenomena (limited by energies and the error margin). In particular, all the UV divergences may be consistently subtracted and all the IR divergences only encode real physical phenomena and the situation when one has asked a wrong or sloppy question.
This (limited) consistency doesn't mean that one should believe that the Standard Model is actually the exactly right theory of Nature up to the Planck scale. There are many reasons to think it is not the case.
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