How to detect a mutation and predict its consequence? I read lecture notes about mutations, and wondered what kind of algorithms are there to detect mutations?
How do we know if the gene is mutated or whether it is a sequencing error?
I saw this thread which is related, but I am not sure how to use the CIGAR information, e.g., is it 100% accurate? What is the underline mechanism to detect mutation? Is there a way to predict what the mutation will cause?
I'll follow up to the great answer from Kamil S Jaron:

Regarding predicting what the variant ("mutation" is a very loaded term) will do, there are a variety of tools. Chief among these are annovar and VEP. The general idea behind these is to classify the variants according to their overlap with genes, which codons they change (if any), how big that change is (e.g., changes in charge are more likely detrimental) and so on. One could also consider conservation, since if a position is highly conserved then changes in it are more likely to be detrimental.

If you really want to predict how a variant will change a protein's function then that usually requires prior knowledge about the proteins in question. Eventually someone will use machine learning to cull the literature and provide good predictions, but I haven't seen that yet.