We just recently got a home inspection on a house we are looking to buy. This is a home which was built by the person living in it, so I believe they took the easy road to many things. Including the plumbing. Two things which bothered me were: there is no vent pipe (stink pipe) and the PVC water lines were used for both the hot and the cold water. (CPVC should be used for hot? )

Anyway, are these 2 major things that will cost a lot of money to repair? And is this something that NEEDS to be fixed? Thanks!

No vent anywhere? Did the inspector look in the attic? How does the plumbing drain? Did they use AAV's? Can't imagine how a toilet would drain without a vent, it would suck all the other traps dry. You can use PVC but it is not recommended. I use CPVC for hot and cold. At the hot water heater, I would sweat a piece of copper to get a couple of feet away and then a male copper to a female PVC adapter. Changing PVC to CPVC , in a crawl or basement space, particularly in a 1 story house is a fairly easy job. The vent could be a real problem, particularly with a 2 story house. You could possibly install a vent to the outside wall and then through the eave, if local codes allow. You see this process in very old Colonial homes that did not originally have indoor plumbing.

Can't imagine how a toilet would drain without a vent, Then let me take you back in time 60/70 years ago. Back in Wisconsin we had lots of homes built in the early century. They were roughed in with one 4" cast iron line, with branches to pick up fixtures, running under the basement floor and then running up to a roof vent. The fixtures vented through the traps. To the best of my knowledge they're still up there.

it would suck all the other traps dry. Not so! My neighbor has a vent that's blocked by Iron chunks that have wedged in the vent and then built up solid but above the kitchen sink tee, The washer uses the same vent. The trap gurgles like hell but still retains a trap seal even when the washer discharges. Since it's working and draining he doesn't want the hassle and expense of opening up his walls.
When I get a complaint like this and the OP want's the easiest less costly to vent the home I advise them to install a AAV on every "S" trap (see image) I would redo the hot lines in CPVC. Good luck, Tom