Recommendations for handling untimely maintenance

I rent from a property management company. I moved in late April and the dishwasher never drained consistently and broke after a couple uses. I notified the landlord shortly after and now it's been a month and three weeks. It took them 2 weeks to get somebody to look at the dishwasher, they ordered a new part for it, and I was ignored when I asked for updates. It took about a month for them to order, recieve, and come back to install the part. Just for them to figure out they ordered the wrong part. The repair company said they could try to expedite ordering the new part but they didn't sound reassuring. It's annoying to not have a dishwasher, but it seems like the sink drains into the dishwasher and sometimes backs it up so if I do a lot of dishes (I cook a bunch) I also have to figure out a way to drain the dishwasher or I end up mopping the floor. The garbage disposal just stopped working correctly today too. This is all on the heels of them failing to fix the blinds (they replaced a couple missing pieces but the mechanism to turn them is broken). I'm so frustrated I'm paying for a place that should include these appliances and I feel largely ignored for the entire nearly 2 months I've had these issues.

tl;dr Is there anything I can do to convince my landlord I need the dishwasher repaired ASAP?