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?