Perhaps this question has an obvious answer, but I have been unable to satisfactorily confirm or refute this. Amino acid translations are in one of three frames (six if considering both strands). In the most simplistic sense, after transcription, the entire exon/intron structure of the gene would be in the same reading frame, and all intron and (coding) exon lengths would be divisible by three. However, based on intron/exon boundary markers, there is no reason (that I can think of at least) that introns should always follow exactly the same reading frame (i.e. have a length divisible by three). Is it possible (and if so, common) for a gene to have an exon in one frame, and the subsequent exon(s) in other frames?
To put some context to this, occasionally I come across gene models that have obviously been mis-predicted. Without re-predicting gene models for a whole contig/scaffold/etc, sometimes it is relatively easy to simply use tblastn with a sequence from a closely related organism to deduce the structure of the gene. Sometimes this results in hits along the length of the sequence, but in different frames (adjacent and always either in the plus or minus frame). Should these be considered to come from the same protein/gene? Instinct says yes, but I have not found anything to confirm.