If you are talking about multiple vias for one connection...
effects/advantages
1effective connection resistance reduces because of parallel connection.
2probability of yield reduction due to spot defect or improper manufacturing greatly gets reduced.
3.in deep sub micron technologies increased cap may be noticed.
You are right, but it's just an example. And it depends on technology. Single via can have quite big resistance, for example in one of newest technologies via between metals can have from 20ohms to 100ohms resistance (source - technology documentation). So even for long connection it can have some significant impact if you use only one via.
Right, but it's not because burning off (for higher currents you need an array of vias anyway), but the minimal overlap used in submicron processes. Already a small misalignment together with some angle tilt during metal deposition may cause metal coverage failing inside the still accessible via wall. See e.g.
I once had a layout person use a single via connecting M1 to M2 in the output metal of a power op-amp. imagine the fun the customer would have had when passing 200mA
through a single via..........