I've finished with the game, but now realize that I never entered that building! I tried once, but some guard told me that I couldn't enter at that point? What is it for? Please feel free to spoil me...

<font color="Orange-Yellow">Hmmmmm. What are jails usually used for??</font>

SPOILER
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If you turn Jan in to the Tax Board Inspector, you can rescue him from the prison later if you want him for your party

<font color="Orange-Yellow">I didn't know that!!!! Well you learn somthing new every day!</font>

Can't blame you ... who would turn our little turnip boy to the IRS

Is it of any use for anything other than Jan and making the Government District more characterised?

Nope, I don't think so. There are a few marked buildings you never get to visit without special NPC quests (especially in GovDistrict).

In theory it's where Keldorns wife should be kept after he turns her in, assuming you take that path, I tried going in to visit, but she wasn't around, still I think she should show up here.

But basically it's just a place added for flavor, and to help you get a second chance at Jan if you turn him in.

Thanks. You do learn something everyday.

I'd like to add that if you are a thief you do the thief-stronghold quest, you get a Thieves' Guild. What you do there is that you are the guildmaster and you send out lesser thieves on missions (bribes,burglaring,assasinations,etc) and then if your
thieves get caught you can go to the jail and bribe the guard to let them out.