Using a grid on a ground AND power supply on a pcb does not cause ground loops, it decreases them. When you're trying to use a shield, you tie one end to ground. Tying two points to ground allows outside signals to flow from one of the points to the other, causing a ground loop and introducing a noise current into the circuit you're trying to protect. This is done because any flow of current causes a magnetic field, which when passing through the wires/circuitry produces a noise current into that circuit.
As for ground/power supply runs on a pcb board, you want the current in path to follow the current out path as closely as possible, to reduce the 'loop size' and thus reduce interference the loop emits or picks up. A solid plane is best, as current can go anywhere it wants, and will follow the supply current. If you can't use a solid plane, then a grid is best. Of course, the mulitpoint star is the best of all, that way you don't have currents from circuit A flowing in circuit B, and vice versa, but this is not always possible, especially in a digital circuit with high density pin counts. When I lay out a pcb board, I route power and ground first. I lay in a grid (both power and ground), verticals on top and horizontals on bottom. Every column, every row. Then when routing I take away only the traces I need to to squeeze signal runs in. Whenever I think about how I'm going to place the parts, I always have ground and power feeds in mind.
Grids are only better than solid planes as mentioned above, if you have a large plane on the bottom and almost no copper on top above it, the board will warp. A way around this is to copper fill a ground plane on top, or even floating copper (not tied to power or ground), and only etch off enough copper to supply a space between runs.
Multilayer is excellent because you get a whole plane for both power and ground.
Also, it is bad practice to run power on one end of the board and ground on the other. They should come in at the same end of the connector and be routed as close together as possible.
When routing high power circuits and low power/sensitive circuits on the same ground, put the high power stuff closet to the power supply, and the low power stuff out on the end of the run. The low power stuff will not interfere as much with the high power stuff and the high power will distort the low power runs. The distortion is called 'ground bounce' and it due to ohm's law (the basic law of current flow). Copper traces have resistance, and current flowing through them will drop a voltage across a length of copper. The bigger the traces, the lower the resistance. This is why decoupling capacitors are placed next to ICs, so they can supply the high frequency hi current draws when the circuits switch, and hold the voltage steady, and then refill from the bus.