We usually use blast/blast for identification of sequences or comparing sequences or for orienting sequences based on reference. Mostly we use it for annotation purpose using publicly available databases. Filtering of blast result is usually based on query coverage, alignment length, mismatch or sequence similarity.

When I use blast it is usually for oxford nanopore reads which did not align to the genome, and I want to figure out if the reads are contamination, from repetitive sequence, of inferior quality or just noise and not real DNA.

I use Blast mainly to aid in typing viral sequences. This info is then copied into a spreadsheet, and there is no filtering involved usually.

I have frequently used BLAT for aligning microarray probes (expression array probes ; generally ~60 bp, Agilent). Most of the times, the objective was to identify the gene it originated from or for the annotation.