Alas most home inspectors don't have a clue and won't warrant the statements they make. It is not possible to tell from your description if a rewiring is going to solve your issues or what it will cost (Though 735 sf is a pretty small house, if there's an accessible basement or crawl or attic that would help a lot).

You should get references to a good electrician in your area and have him come out and inspect your wiring. Don't be afraid to ask questions. Questions are:

1. Is the wiring safe?

2. Can something be done about the capacity issues with your appliances.

3. What's going on with the lights.

Are these traditional bulbs? I suspect if so, it's probably vibration that's killing them. You might try rough service or an LED or CF. If it's a CF bulb that's dying...the problem is likely heat. Again your electrician can help.

the house was built in the 50's

does the house need rewiring?

Yes

Is rewiring expensive?

Yes but worth it. It doesnt sound like your wiring is safe at all and you are at a fire risk.

You will most likely need a new panel, I am guessing you have a fuse box nearing the end of its life. Running new wires to get proper grounds and the correct amount of circuits will make your problems end. There are so many things probably wrong with the current electric, its best to just redo. The new panel alone will be at least 3-4 grand (due to the increased cost of arc fault breakers) and the labor/materials for the rest of the house will be extra.

Things to ensure are done.

20A GFCI separate circuit for outlets in each separate bath. 2-3 separate 20A GFCI circuits for kitchen receptacles. Separate circuit for fridge. Separate 20A circuit for microwave. Separate 20A GFCI circuit for dishwasher. GFCI circuit for laundry room. Everything else is pretty standard. They will have to provide arc fault protection on everything now also, which very greatly reduces the risk of electrical fires. Better to just request 20A lines throughout, it is not that much more.

Note vith's guidance is widely accepted but deviates from the NEC. Again, you need a competent electrician to appraise the situation. Get multiple bids and REFERENCES.