Looking at the tank it is fairly typical of the state of most tanks I come across while doing Legionella risk assessments
Your Landlord may have done a Legionella risk assessment on your property which may or should have recommendations, you could ask to see it.
How safe it is would depend on what the tank supplies, if it is only hot water and the hot water temperature in the cylinder is high enough to kill off anything harmful, it is probably safe to use, without seeing the entire system I cannot be definitive. its not ideal and should be sorted. Ie cleaned, fitted lid and lagged.
It was probably fitted before the bylaw 30 tanks were bought in, which included lids lagging fly screens etc, you will always get some build up of scale depending where you live which does need to be cleaned off
If you want to read up more on Legionella hopefully these links will work.
Provides links to sources of information and guidance on health and safety in the health and social care services sector.
www.hse.gov.uk
The law is clear that if you are a landlord and rent out your property (or even a room within your own home) then you have legal responsibilities to ensure the health and safety of your tenant by keeping the property safe and free from health hazards.
www.hse.gov.uk
Legionnaires' disease - Technical guidance - https://www.hse.gov.uk/pubns/books/hsg274.htm on this page look for part 2 of hsg274 as a pdf, download it
it shows various examples of tanks and recommendation action page 25 onwards
good luck