So I completed the quest line that destroys Heimskr's house in Whiterun so I can't complete one of the jobs for the thieves guild. Will this hinder my game?
Edit: you need these quests to upgrade the thieves guild, so I am assuming I will never be able to fully upgrade.
No, it will not hinder your game.
As for the second part, what do you do since you can't go into his house to complete it?
Simple, cancel it with Vex/Delvin. You will fail the quest that you are on, but it will give you no penalty, and you can just get another one.
A good trick is to sit there and cancel quests for cities that you have already done special quests for, and/or cancel until you have both quests in the same city.
See UESP for more details on these types of quests.
Heimskyr's house is not part of any main Thieves Guild quest- only the radiant quests. These quests can be cancelled and replaced by talking to Vex or Delvin.
