Does the fact that we cannot exactly solve the Standard Model undermine the validity of QFT? I have seen discusstions of this types before: there is a question about photons or virtual particles or vaccuum, etc. And there is usually a good and  clear explanation from the point of view of Quantum Field Theory (QFT). It is usually final and mostly accepted answer.
But it is sometimes happen, that someone mentions the fact that the Standard Model (SM) gives only approximated predictions. Physicists need a perturbation theory to make predictions for collider experments and that results in some uncertainties. Espectially when ineraction constant is not very small so the series converges slowly. 
As I understand the logic of this arguments - that approximate nature of SM preditions somehow undermines the basics of QFT. So the answer to the initial question (about photons or virtual particles or vaccum, etc) is said to be not based on a strictly experimentaly proven theory.
But I cannot see how one makes this logical connection between the statements about SM and about QFT. I suspect that this step is flawed, but I can be mistaken. Do you think there is such connection? 
 A: First: Scientific theories are never proven, only not falsified. Repeat that until it sinks in.
Now, for the actual content of the question: That we only have perturbative ways to compute the S-matrix/scattering amplitudes for the Standard Model is not a reason to doubt its validity. Almost no physical system, apart from toy models, can be solved exactly, there are, for almost every real world situation, approximations involved.
Think of the humble pendulum - even for this silly mass hanging from a string, you almost always will assume the string to be massless and $\sin(\phi) = \phi$ for small angles. This does not mean that the physical description of classical mechanics underlying this is "invalid" (well, it is, since we know of quantum theories, but that is not because the pendulum is not described exactly).
Almost all complicated systems have to be approached perturbatively - start from the simple model you know exactly (most often the harmonic oscillator, which is also the starting point for naive QFT perturbation in a sense), and see what happens if you add (small) complications. This doesn't mean our description of these systems is flawed, it means the real world is damned complicated.
A: QTF is pretty messed up, although many physicists won't probably agree with this. The current methods are good enough to predict outcomes of experiments, but they are quite dubious from a mathematical point of view. Consider Dirac's interaction picture for instance, which is usually invoked by many physicists around the world to predict the outcome of an high energy experiment or to verify that such results are comparable to the known theory. Only problem is that the interaction picture doesn't exists, even for a free scalar field with no interaction at all! (cf Haag's theorem). This fact is usually swept under the carpet, and therefore the ill-defined interaction picture is still broadly used to compute stuff.
