In Solitude I've purchased a house from "Falk Firebeard" and spoke to "Jarl Elisif" and she mentions there's a new place in her court for a thane. Now after I agree to help 5 people in Solitude obviously due to previous actions it shows as 5/5. But when I speak to "Jarl Elisif" it does not show as complete even after she grants me a new house carl.

What should I do for it to show as complete?

This is the eighth bug/glitch I've experienced through out my game and it's extremely irritating! Help please?!?!

Same happened to me on this character. However I didn't bother with it because the quest finished anyway and I became Thane and bought the manor in Solitude. I have had a few finished misc quests finish and then get stuck in my journal. As long as they worked, I ignore them.

Off Topic:
Another strange glitch I had on this playthrough was the fact that the Altmer lady from the clothes shop in Solitude and the Executioner both disappeared right after I went there the first time. I didn't have Dawnguard installed yet and hadn't done the MQ either, so no Dragons. They simply vanished from the face of Nirn....LOL

If on PC you can use the console command

player.setobjectivecompleted favorjarlsmakefriends 30 1

On XBox and PS/3 completing a sixth favor should fix the problem.

Yeah I had one yesterday for the "Bards' College" where he has to read out the verses from king Olaf's book to "Elisif" and she had disappeared completely. I assumed this was because of the temporary peace treaty so just finished the main quest.

But there's too many.

Does anyone reckon there'll be a DLC where you can improve your character's level above "Level 81"?

Good idea, I'll take on the quest to assist 5 people from a previous load, go down to the docks and do a sixth one and see what happens.

Thanks