Mousseline, the first thing to understand is the Agent is only concerned with one thing... yes, you've guessed it, MONEY! in the form of letting fees.
They said the property was fit to let and gave you a rental income as high as they could so that their profit (assuming its a % not a fixed amount) could be higher. This despite you telling them you wanted to 'sort a few things out'.
They then put in the first tenant who was wiling to sign the contract (which the tenant did) - no doubt with the Agent promising that they would have you sort out any subsequent problems which the tenant mentioned on the inventory. Again this was probably the things you told them you wanted to sort before letting!
Then, the Agent started acting on behalf of their tenant by informing you of stuff that needed fixing ACCORDING to the tenant (not the Agent) and most probably based on the responses to the inventory list which again is most probably a standard one, not one tailored to your property.
I let a house myself and don't use an agency because in my past experience they don't do half the stuff they are supposed to do and when they do its only half-hearted.
I also had a video inventory done of the whole house which the tenant then signed and was given a copy of. This is unique to my property and therefore the best defence against subsequent claims at the end of the tenancy.
As far as maintenance is concerned, if you can't undertake the work yourself or have your ?husband do it then find yourself a local tradesman by recommendation from a friend or use Check-a-trade.
There are several landlord associations which you can join for advice and legislation guidelines on all aspects of letting - some of which are legal requirements which you (not just the Agent) need to be aware of. They will advise you on ALL aspects of letting and more than cover the work the Agent is undertaking and charging for - this will be cheaper than the fees you currently pay.
You can still use an agent to find a tenant if you want/need to.
The Residential Landlord's Association and the National Landlord's Association are just two of these and the costs are minimal for the return (about £80 per year) all tax deductible.
If you must use an agent then these bodies (RLA and NLA) will have recommendations for GOOD agents in your area based on member satisfaction.
As for your current issues, then the advice given by previous posters about it fit for habitation is good advice and you only need to ensure the property remains habitable - as it was when it was let!
Best of luck!
Steve B