stamp duty penalty

If you instructed him to pay the stamp duty or he neglected to do so.

It is a genuine apeals procedure but simply forgetting to pay is not a valid reason for an appeal AFAIK.

The upside down parking disk story is something of an urban myth. Locally a big fuss was made by a woman who repeatedly claimed she was "victimised" for such an infringement. In fact what she had done was to display the badge (Not the time disk) with the wrong side visible. The side she displayed was not the one that has the serial number and expiry date on it. Thus she was ticketed because the traffic warden was unable to see if the badge was current or not. Thus the ticket was corretcly issued.

The SDLT return should have been submitted within 30 days of completion of your house purchase, late submission results in an automatic mandatory fine of 100.

DKCC

But this only applies to DIY conveyancers. If you use a professional, it's part of their job to deal with SDLT on your behalf, and if they screw up, they are liable to pay the fine on your behalf too.

Legally liable?

Yes, of course. Only indirectly, mind. The liability would be by way of compensation for breach of contract for failing to exercise due diligence or whatever it's called. Paying the SD is part of the package. The DIYer might not know and fall foul, but the professionals are expected to know, and either to deal with it or to make sure their client knows they've to do it themselves.