One of the most important things to remember about making a custard is to temper those eggs! It's a simple procedure, but critical, and many recipes do not mention doing this.
To temper eggs, all a cook needs to do is to add about a teaspoon of the hot mixture to the eggs (which are in a separate bowl) and stir. This warms the eggs and will keep them from scrambling when they are added to the custard itself. I've never had my eggs scramble in a custard if I temper them first, and I've made a good many custards from scratch. You do need a double boiler of some description to do them right, though. Whether it's an actual double boiler, or a bowl over a pot of water, using one it really does make all the difference in how a custard turns out.
If you have doubts about the eggs, you can always strain the custard, and no one will ever know the difference. The eggy bits will be left behind.