I want to rent a flat in Montenegro for 2 persons for about one month. Is there any problem I should be aware of (I heard in some countries you need to have a job or local bank account to rent a flat).
Long-term rentals everywhere around the world typically require the tenant to prove the ability to pay the current and every future month rent. This is done by showing salary slips (usually the last 3 in France), payment receipts from previous rental agreements, a reference letter, and/or binding someone else to be your guarantor to cover any missed payments (this person too will have to show proofs).
Short-term rentals on the other hand are often bound by simpler contracts (if any) which involve up-front payment for either the full rental period, or blocks of several consecutive months. No need to ask for proof of payment ability if the tenant pays everything in advance.
Now I don't know about Montenegro specifically. Going out on a purely speculative limb though I would say that since Airbnb does have various short-term rental listings for Kotor, montenegro, it should be easy to rent a flat in Montenegro for a short period of time without having to worry about proof of employment and other bureaucracy.
For completeness sake note that a gazillion other rental websites exist out there. Here on TSE we don't really do recommendations, hence the answer to
what would be a good site for renting a flat in Montenegro (in the bay of Kotor)? might be off-topic here.