Fixed-term vs. unlimited
Unlimited is standard and better for you. Fixed-term leases need a legitimate reason (planned personal use, renovation). Without reason, the limitation is invalid. Watch out for chain limitations.
Cosmetic repairs (Schönheitsreparaturen)
The famous painting clause. Many old clauses are invalid (rigid schedules, taken over unrenovated). If in doubt: Ask tenant association. New trend: Landlord renovates, you pay higher rent.
Utilities (Nebenkosten)
What's in warm rent, what's extra? Heating, water, garbage, janitor, insurance typical. Electricity, internet, GEZ always extra. Advance payment or flat rate? With flat rate no back payment - but no refund either.
House rules
Part of the contract. Regulates quiet hours (usually 10pm-6am), stairwell cleaning, grilling, pet keeping. Read it! Violations can lead to warnings. Some rules aren't enforceable (blanket pet ban).
Negotiating special requests
Permission for pets, subletting, renovations - better to clarify before signing and put in writing. Getting permission later is harder. Attach anything deviating from standard contract as addendum.