Good analogy, faulty reasoning on the landlord's part. You can only be responsible for taking care of the place and utilizing it normally. If something is damaged, then you can be charged to fix or replace it. If the blinds are "sticky" were they that way when you moved in? Did you break the blinds? By break I mean smash them to pieces or cut them up? You cannot be expected to de-stickify blinds that were sticky when you got there. You can be expected not to break them.
The sink issue is interesting; it would be especially interesting to see if he sued the previous tenant for the damage to the sink but failed to fix it before you moved in.
You cannot be expected to be the carpet faith-healer. You can take care not to soil or damage the carpets, but at the end of your tenancy, if you have not committed damage on the carpet, arguably it is just wear and tear. In this climate, carpets get grotty no matter what you do, even if you never spill anything on them.
The important thing is to be ruthless when you fill out the walk-through checklist at the beginning of the tenancy, and take a lot of pictures when you move out. It is also patently unfair to be charged for damaging something that is not called out in the move-in walk through checklist.
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