About the crime, Romania is a civilized EU country and you are safe. The border officers are susceptible to bribes, especially since you have foreign plates. There were recent controls/arrests, one of the measures in order for Romania to qualify for Schengen (which didn't happen yet).
There are very few sections of highway (1), so the traffic might be congested and many roads have potholes.
After years of driving in Romania, I would recommend :
Do not forget to buy a "rovinieta" (vignette, road tax stamp), even for one day : it is mandatory not only on highways, but also on many "national roads". The control is automatically done with camera systems, and you could have problems when leaving Romania to Bulgaria if you have not recorded your car. Take care also on Bulgaria : they do have a tax stamp system (like in most of eastern Europe countries). You can pay for these stamp at the border when entering in the country, or in gas stations.
Some have already said it : the heavy truck traffic can be a big issue, mostly if you drive through Transylvania which is a very mountainous area. Just let them overtake.
In countryside, you can meet, even on large road, some horse cars, many dogs (and other animals), bikes, and pedestrians (especially when crossing cities). Most of the time it will be OK because the road are clean, and the speed is limited. But if you drive at night, be careful. The exact same conditions apply for Bulgaria.
I have not seen any crime problem, nor border patrol or policemen asking for bribes. Just respect the speed limit, drive "normally" and everything will be OK.
People are very nice, and the countryside is amazingly beautiful. And because the country is still a bit "savage", some roads are magic like the Transfăgărășan which I recommend if you have time for it and if you drive around Sibiu.
Since all the romanian politicians agreed Romania does not need motorways/freeways, these are short and far apart. So, plan for an average of 60Km/h (37mph) on most roads.
The main roads between larger cities were upgraded to expressways in the last 10 years but since it is an upgrade, you'll often find bicycles, tractors, horse-drawn carriages on them.
If driving at night, be very careful because most of these slow moving vehicles are not sporting any lights.
Another hazard is the number of reckless drivers, often driving high-power cars.
Plan also for a very large number of lorries/trucks during the working days and even on weekends.
Since lorries are forbidden to drive in Hungary during the weekends, most drivers will drive through Romania during Sunday evening towards the Hungarian border, so plan accordingly for increased traffic towards Hungary.
Do not cross the continuous line in the middle of the road when overtaking, even if the locals do it. The police is eager to fine drivers of foreign-plates cars when doing it.
I recently drove through Romania and Bulgaria on motorbikes and didn't find much problems. Like most eastern European countries the quality of local driving isn't great, especially compared to western European countries.
There were a lot of trucks and lorries on the roads. Aside from that it was fine.