Summary

The answer would seem to be NO, from the very fact that the vaccine works. My answer discusses why this should be so. It takes a somewhat different tack to well-documented, but different, answer from @endolith.

Answer

The term ‘wobble’ was originally introduced by Crick to describe and predict instances of non-Watson–Crick base-pairing between the 3′- base of a mRNA codon and the 5′-base of a tRNA anticodon. This was provoked by the finding of the base, inosine, at the 5′-anticodon position of some of the first sequenced tRNAs, and other examples (such as a 5′-anticodon G being used to decode both 3′- codon C or U) were found in situations where the pair of codons involved specified the same amino acid. (See also this SE answer)

The term ‘wobble’ was specifically applied the base pairing at this position as it did not occur at the other positions, where it would generally cause the incorporation of the wrong amino acid. Moreover, when the three-dimensional structure of tRNA was elucidated an explanation for this was found in the strong base-stacking at the 3′- and preceding anticodon position, but not at the 5′-anticodon position (see G34 below — explanation in answer cited above).

Nevertheless, the term ‘wobble’ is sometimes used to mean any sort of non-Watson-Crick base-pairing, which can be the cause of ambiguity in cases where the context does not clarify the situation. I shall try to be clear in this answer.

The question is concerned with the possibility of non-Watson–Crick base-pairing — and consequent mistranslation — between tRNA and m1Ψ (N1-Methylpseudouridine — above) at codon positions 1 or 2 in the artificial Covid spike protein mRNA used in the Pfizer and Moderna vaccines. I would suggest that this does not happen to an appreciable extent otherwise very little spike protein would be produced and the vaccine would be ineffective, which is certainly not the case. The developers of these vaccines were clearly aware of the possibility that m1Ψ in the mRNA might have a greater mispairing potential than the unmodified U it replaced, as they changed a number of codons in consequence. However these changes were specifically U→C at the 3′-codon position (red shading, below), as the tRNA that decodes cognate pairs of codons ending in U or C always has a 5′-anticodon G. Of course, it would have been very difficult to do anything if there were miscoding of m1Ψ at the first two codon positions, but one can assume that the developers either checked that this did not occur or guessed correctly that it would not occur there to an appreciable extent.

A possible objection to the above argument is that readthrough of termination codons (UAG, UAA, UGA) occurs to an increased extent in mRNA in which m1Ψ has replaced U at the 5′-codon position. (This may be one reason for the use of multiple termination codons in the artificial mRNA, although it was not mentioned in any answer to the SE question on that topic.) However the situation here is different from the miscoding of, say, tyrosine codon UAC. In that case miscoding would involve competition between the tRNA for tyr and those for his, asn and asp (see green shading, below). However termination involves competition for the codon between tyr-tRNA and the termination factors. The modification of the codon U may conceivable decrease its affinity for the termination factor, which depends on RNA–protein interactions, not base-pairing.

Summary

The answer would seem to be NO, from the very fact that the vaccine works. My answer discusses why this should be so. It takes a somewhat different tack to well-documented, but different, answer from @endolith.

Answer

The term ‘wobble’ was originally introduced by Crick to describe and predict instances of non-Watson–Crick base-pairing between the 3′- base of a mRNA codon and the 5′-base of a tRNA anticodon. This was provoked by the finding of the base, inosine, at the 5′-anticodon position of some of the first sequenced tRNAs, and other examples (such as a 5′-anticodon G being used to decode both 3′- codon C or U) were found in situations where the pair of codons involved specified the same amino acid. (See also this SE answer)

The term ‘wobble’ was specifically applied the base pairing at this position as it did not occur at the other positions, where it would generally cause the incorporation of the wrong amino acid. Moreover, when the three-dimensional structure of tRNA was elucidated an explanation for this was found in the strong base-stacking at the 3′- and preceding anticodon position, but not at the 5′-anticodon position (see G34 below — explanation in answer cited above).

Nevertheless, the term ‘wobble’ is sometimes used to mean any sort of non-Watson-Crick base-pairing, which can be the cause of ambiguity in cases where the context does not clarify the situation. I shall try to be clear in this answer.

The question is concerned with the possibility of non-Watson–Crick base-pairing — and consequent mistranslation — between tRNA and m1Ψ (N1-Methylpseudouridine — above) at codon positions 1 or 2 in the artificial Covid spike protein mRNA used in the Pfizer and Moderna vaccines. I would suggest that this does not happen to an appreciable extent otherwise very little spike protein would be produced and the vaccine would be ineffective, which is certainly not the case. The developers of these vaccines were clearly aware of the possibility that m1Ψ in the mRNA might have a greater mispairing potential than the unmodified U it replaced, as they changed a number of codons in consequence. However these changes were specifically U→C at the 3′-codon position (red shading, below), as the tRNA that decodes cognate pairs of codons ending in U or C always has a 5′-anticodon G. Of course, it would have been very difficult to do anything if there were miscoding of m1Ψ at the first two codon positions, but one can assume that the developers either checked that this did not occur or guessed correctly that it would not occur there to an appreciable extent.

A possible objection to the above argument is that readthrough of termination codons (UAG, UAA, UGA) occurs to an increased extent in mRNA in which m1Ψ has replaced U at the 5′-codon position. (This may be one reason for the use of multiple termination codons in the artificial mRNA — see this answer to the SE question on that topic.) However the situation here is different from the miscoding of, say, tyrosine codon UAC. In that case miscoding would involve competition between the tRNA for tyr and those for his, asn and asp (see green shading, below). However termination involves competition for the codon between tyr-tRNA and the termination factors. The modification of the codon U may conceivable decrease its affinity for the termination factor, which depends on RNA–protein interactions, not base-pairing.