The Doctor wrote:

About Sherlock starting paying attention to the grammar because he was bored: I read it differently in so far that Sherlock quickly deduced that the man actually did commit the murder. Thus he had no interest in getting the man of the charges and concentrated on correcting his grammar instead.

Yes, my comment about Sherlock seeing how long this guy could keep his cool related to that.
This guy lost his temper quickly with Sherlock over simple grammar corrections. As the guy himself said, he lost his cool with his girlfriend over something more 'delicate'. It doesn't take Einstein to work out he'd lose his cool enough to strangle her, accidentally of course.

I think he said he stabbed her "over and over and over".   Accidentally of course 

I think Sherlock had determined within the first moments that the guy was a common, woman-hating, moronic low-life and the case held no interest for him.  He toyed with the jerk, got him to snap easily, and 'boom' - outta there and home on the next plane to London.

I wondered about the murdered wife Karen.  She would have been British too, right?  So if she was British wouldn't Barry Berwick have been sent back to Britain for trial instead of facing Belarus justice.  Maybe I just don't know anything about international law.

But I do know one thing  - I love that scene and I don't ask for too much realism from it.  It was black comedy at its best.

If the crime had been committed in the UK and he had escaped to Belarus then he may have been brought back to the UK for trial. However, as the crime took place in Belarus the the trial would also take place in Belarus and he would be subject to Belarussian law.

Haven't scrolled back through the thread, but apart from us actually seeing the scene where the convict is trying to engage Sherlock's services...he and John later engage in a discussion about the case.