There is no standard for this, and performing this manual inspection requires experience more than anything else. However, as I recently did this for a private company in New York, USA, I can share my own experience.

That of which to be aware:

• overall read depth over the variant position. For a germline variant, technically, my work from the clinical setting in the NHS England shows that 18 is the bare minimum that one should want, with 30 being ideal.
• read bias - is the variant mostly called in R1 or R2?
• position bias - is the variant called at the end of reads?
• quality of reads - are the reads flagged in IGV for any reason?
• MAPQ of the reads
• are there many base-mismatches in the reads aligning to the general region surrounding the variant, and/or indels with a seemingly sporadic / random distribution?
• is it a repeat region, or do any reads span a repeat region by even a few bases?

Probably more criteria about which to be aware.

Kevin