Spend a bunch of time thinking about the mechanical nature of the PCB. Fancier software that does 3D pix can help if you have trouble visualizing the finished product.
Clearance for mounting screws? Include the head and tool space requirements also. Are heavy parts (transformers usually) near the mounting holes to avoid board flexing? Connectors also: if far from a mounting hole, inserting and removing high-force connectors is difficult if the board is springy, and could stress or even crack a PCB trace. Access for fuses, trim pots and those type of parts need to be considered. Are ribbon cables routed to clear the components? It's hard to work on or probe a circuit if a ribbon cable is covering up the whole top. Consider the tools you use to work on the circuit board. Can you fit your soldering iron in between two very tall capacitors to change a 0803 resistor? Do you have places to touch a meter or scope probe if you need to debug? Some small SMT-t0-SMT circuit nodes may not even allow you access to the conductors somewhere unless you add a test point.
How about cooling air flow for higher power components? Try to avoid aligning inductive components, wire-wound resistors and such to avoid overlapping magnetic fields.
These are some of the things that I think are important to a well-designed PCB, but are generally seldom discussed in PCB design. Usually it's all about circuit traces and complicated inductance/capacitance issues, but sometimes the basic stuff can sometimes cause you just as much grief. If making many boards or multiple revisions - absolutely put the revision number and/or date on the silkscreen. If not using silkscreen, put it onto a bare section of copper.
I like to put in a few extra parts (especially if this is a prototype design) in case I need to make changes, such as adding a capacitor for unexpected filtering. Perhaps a 2nd resistor in parallel to tweak a resistance that I thought needed to be 1000Ω but really needs to be 763Ω. I also like to add two small grounded holes near the edge of the pcb. I solder in a short U-shape bare wire and that makes an excellent point to attach a ground clip for a scope or meter. I always provide an easy point to measure power voltages also. In some cases where a power supply is on the board, I split the power trace between the source and the load, and use a small wire jumper soldered in place. That allows me to cut the wire and measure the current draw exactly. When I'm done I solder it back in.
Another potentially big thing - mostly for prototypes - is to NOT connect logic inputs directly to ground. You might some day realize that grounded enable pin needs to be disabled somehow, and unless you have a DIP package, lifting a pin may be impossible or difficult at best. A short 2-3 mm length of trace before contacting the ground plane will not usually cause electrical issues, and will allow you a place to use a xacto knife or drill to isolate the pin from ground, then use a tack-soldered wire.
Some parts are sometimes hard to get. For a lot of larger capacitor thru-hole sizes, typical lead spacings of 2.5, 5, 7.5mm etc. may not always be available. I'll often overlay PC part patterns of several sizes at once, so no matter what size I end up finding, it will fit into the board with out a lot of funny lead bending. For transistors that sometimes have different pin outs: EBC or ECB, I use a "special" hole pattern with "ECBE" which allows different types to be inserted either forward or backwards without a lot of crazy lead twisting. You can't make one board that handles every possible part, but for some odd, unusual and difficult parts to find, putting flexibility in the PCB is sometimes a good time saver.
Concerning the electrical issues, ground is often a problem. Don't think of your circuit as just current flow going from power supply to components and then ground and that's all. Think of the ENTIRE CIRCUIT. Electricity 101: current flows in a loop. Think "Current flows through various components, eventually to a ground and then back to the power supply." If you think like that all the time you will more likely consider the ground currents that will be flowing into your PCB's ground plane. If you merely think "...all this relay current flows into the transistor and to ground..." and that is all, you'll assume all ground is perfect. Think also of the current path from the transistor back to the power input connection, and make sure the 'trace' is short and thick enough, and the supply at that point is adequately bypassed.
And one more thing: good luck!