ExAC Browser: What does a "dubious variant annotation" mean?
Briefly speaking you expect more or less uniform coverage for reads. So if you see a systematic difference in quality scores or coverage for minor and major alleles or for forward and reverse strand, it could be an SNV, but most likely it is a technical issue. That's a 'dubious variant'.

A lot of such biases are described in "Genotype and SNP calling from next-generation sequencing data":


  Other types of filtering based on deviations from the HWE — generally
  low-quality scores, systematic differences in quality scores for major
  and minor alleles, aberrant LD patterns, extreme read depths, strand
  bias, and so on — can also help to improve the accuracy of genotype
  and SNP calling. The appropriate filters depend on the sequencing
  protocol and the upstream analyses. For example, a site with strand
  bias (where a disproportional number of plus and minus strands are
  observed) could be an indication of a problematic site that is more
  error prone and should be filtered out. However, if the sequencing has
  been performed on captured sequences, such as those used for exome
  capturing, then the bias might not be an indication of a problematic
  site but rather an artefact of the capture array.


Update
I've just received an answer from ExAC:


  The "LC LoF” means that the variant was marked as a low confidence
  loss of function variant. If you click on the “Transcripts” dropdown
  on the variant page it will show the reason why the variant is of low
  confidence for that transcript. In this case it was flagged as
  “END_TRUNC”. An explanation of the LoF filters can be found here:
  https://github.com/konradjk/loftee