I've just watched series 2 in full. (Not seen first season as watched 2nd with Mrs as she'd seen the first, but they are completely different cases). My thoughts are that it was a real eye opener to jury service which I've never done.
To answer the OP, we can't have "professional" jurors because there is no such thing. How would you define one to be so? A jury is meant to be a snapshot of society including people from different backgrounds/experiences/lives in order to average out views and hence decisions.
Having said that, I take major issues with some of the people that were on that jury. Now, most of the issues are just to do with their characters which can't be changed (more on that below) but what can be changed, is people should be told in general terms what the case is about and then asked again whether there are any reasons as to why they would be bias. As an example, there was a women on there that had pretty much took pity on the women from the first minute and was always going to vote for acquittal. What did she do for a living? She worked with domestic abuse cases FFS.
Then there was another couple of women who were speaking of major previous domestic issues. There was also 2 guys who had also suffered previously with similar.
There were a couple of people that very stubbornly had made their decisions early and were very closed minded. They bullied and over voiced other people when their opinion was challenged. I feel that less strong, more introverted people are less likely to offer their full opinion in the climate of the room with shouty, "I'm right" types. It was really concerning to see how stupid some people can be as well.
Overall it left me concerned that the AVERAGE jury will contain people that are simply unfit to form reasonable opinions (BASED ON THE INFORMATION GIVEN) in a team, but I don't have an answer or solution, other than to introduce basic aptitude tests and/or filter based on conflicting past experiences.