When wiring a European (Schuko) plug, what thing should I focus on not to mess up?

I assume the plug uses screw terminals. In this case, and if you use stranded wires, use wire ferrules to protect the wire strands from breaking. The wire must be rated for 16A usually. Ensure that the strain relief is tightened properly. Make the earth/PE wire little longer than N/L. This is to ensure that the PE wire stays connected longer than N/L in case someone manages to pull the cable out.

As obvious as it gets, but better safe than sorry, and I've re-done enough such DIY plugs to think this is answer-worthy:

• make sure that the strain relief presses on the outer jacket (the outer jacket should reach 2-3 mm beyond the strain relief "bridge")
• cut the L and N wires ~1 cm shorter than the PE wire, then bend the excess PE wire so that it will detach last when the cable is forcedly removed from the plug
• use suitable pointed pliers to arrange all three wires neatly around the threaded studs that will later take the screws from the top part of the plug assembly (often insulation is damaged by squeezing between the plastic parts, or even the screw, which can be really dangerous with cheap models where the case screws are accessible while the plug is in the socket - the plug casing is plastic so no PE protection here).
• test the cable after assembly, with a load close to its rating (for example a 3000 W radiator)

Note that neither SCHUKO nor EN 60204 (VDE 011) explicitely mandate solder or ferrules on stranded wire - but using ferrules is common practice and should be standard whenever a screw is used to clamp on a stranded wire.

Tin-coating may seem a cheap alternative to ferrules but is difficult to get right and dangerous. For the last 15 years I've seen no professional electrician in Central Europe practising it any more.

A peculiarity of SCHUKO is that "polarity" does not matter - there is no marking for where the L and N should go because plugs are not directional like for example the British ones.

If you don’t have any ferrules handy and, from experience, most ordinary people don’t, then I tend to bare about 12mm of wire, twist it gently and then double it back on itself - then put it in the terminal and tighten the screw.

Only time one has come out on me was when somebody pulled so hard on the cable trying to pull the plug out...