I don't know if this will be any help, or just more confusing but here's my own experience.
Depends what you mean by "over the counter"... I know 23&me has gone the route of literally over the counter, but online you can purchase a variety of things.
I did 23&me and can't recall anything unusual showing up. In terms of chromosomes, they only test?report? on what you have given them as your sex. (Does that make sense?) If you register as female they only do X, if you register as male they will do X and Y.
They also only test a small number of snps, really small % but do give some mitochondrial DNA results (I'd guess any ancestry-marketed test would)
Then I got full exome sequencing with Genos.
That was more about looking into some other things like my collagen issues and stuff.
Yup there were some potential sex-related mutations flying around (still trawling though that) but what it did do (courtesy of their method of sequencing I'd imagine) was produce some Y results in my raw data.
Which was a bit of a surprise to me given I'm anatomically female (so must likely be XXY but with something else that meant I didn't end up Klinefelters - maybe missing the SRY gene or summat not enough info to know since it was exome-sequencing not full genome). It didn't show on their own website thingy that you can use to look at variants etc. I emailed back and forth with them, and they contacted their <can't recall the word> team to try to see if there had been any mistakes in compiling my data. They also said the web interface only gives the results for what I identified myself as. The raw data was different/full. And I only found it because.... you don't get *much* in the way of interpretation of variants from these companies. You have to run it through various other websites and softwares etc to really get into it, VEP/ensmbl, plenty of linux and R programs out there, things like Enlis and Promethease. On and on.... checking with ClinVar, OMIM, NCBI listings.
It was looking at the VEP results that did it. Ran the program and mulling through the results when I realised that last ones I'd written down were given as located on the Y chromosome. I have the large letter WTF??? underlined several times, in my notes!
So I found out mine by accident rather than purpose.
As other's have said, for chromosomal issues you need karotyping, not exome/genome sequencing.
And exome/genome sequencing only gives you the DNA sequence, point mutations, snps/snvs (single nucleotide variants) no information about things like copy number variations or structural variantions so it misses out quite a lot f data there if you are looking specifically for abnormalities. I've tried looking into the not-terribly-accurate computer programs etc for determining copy number from exome sequencing from BAM files (since you get paired-read and read-depth, pile-up data with Genos), but it's beyond my computer abilities!!
One of the advantages of Genos was that you do own your own data. But the exome sequencing doesn't include mitochondria-DNA.
