Should the covers on sewage drainage pipes be airtight?
The risk is that you have sewer gas escaping at ground level and this could easily enter your house. This gas is potentially flammable or explosive. 

Venting issues are not going to cause a backup. Slow draining or gurgling are common symptoms of venting problems. If you have a backup it is very likely your sewer is clogged. 

There are also environmental concerns with discharging sewage on your lawn in that it can enter the drinking water supply. I imagine you could be fined for this.