This state is on the Landlord, not the previous tenant.
The tenant moving out is answerable to the LL for the condition.
Then it is up to the LL to get the property into lettable state, regardless of the condition they took it back in.
So, between let’s, LLs nearly always have to do something...it’s part of the job. That would often be a refreshing of paint where there are scuffs, perhaps new carpet every 5-7 years, some gardening, could be more major work such as a new bathroom or boiler. Everything should work and be clean.
The LL is responsible for the property having a window which doesn’t close and for the stuffs to the wall and dirt and stuff left behind, even if the previous tenant did all those things, in terms of the current tenant.
I agree about getting the agent to come and look with you as it will be hard to say any of it is acceptable. As I said before, email them and the Landlord every day listing everything which is unacceptable. Start going doing the agents official complaints procedure and make it clear you will take it further if you don’t get satisfaction.
I agree this is a slum landlord ...a rogue. You might force a few minor improvements gradually, but someone who starts like this is not going to be a landlord who meets the obligations you pay for...they aren’t going to respond quickly to issues and send workmen fast and without quibble if the boiler breaks, or take it as their responsibility to always provide a habitable property. This will be a constant battle and you will be treated as a nuisance, rather than as a paying customer who is entitled to what they have paid for. On this basis, I would look to give notice at the 4 month point (assuming you have a 6 month fixed term contract) and leave ASAP. As you have moved in and the tenancy has started, you are now committed.
It would have been better not to move in....but I appreciate it’s easy to say that and not so easy to carry it out if you have nowhere else to go and no money left because the rogue landlord has your deposit and first months rent.
Buyer beware. Inspect very carefully close to the move in date. Do not hand over money until you’ve done that. Do not move in if the condition isn’t satisfactory. Always go to the property with the agent or landlord so you can go round the property together to do an inventory and condition report. Insist on these things and don’t deal with LLs or agents who just want to give you the keys, or take money for a property you havent seen or only saw ages before the time for moving in. Always aim to speak with the LL even if an agent is involved as you can gauge them, as well as them gauging you. Ask for references from previous tenants. Avoid this kind of nightmares which OP is now in for months minimum.