Mounting components on both sides of a PCB

First off, use a 4 layer board. Not only does it make layout easier but inner ground and power planes provides a barrier against front/back crosstalk. Also, 4 layer is not much more expensive than 2 layer

Second, lines crossing is nowhere near as bad as lines running parallel

Adding to Dirk's Answer

Be aware, mounting on both sides of a board may not buy you as much real estate as you might be imagining.

When it comes to board density, your ability to route traces tends to be a critical factor as density goes up. More layers helps, but then you fill up space with vias.

Double sided tends to make it MUCH harder to route unless you use buried or blind vias and use many MORE layers. The cost tends to go up a notch or two and reliability goes down.

A common trick though is to save room by putting small things like decoupling caps/pull-ups etc on the back. Since the power lines normally have vias close to the chip anyway, flipping them to the back is not so bad. If you have to add vias to do that it is pretty much a wash.

Also you need to be very aware of thermal issues, you do not want a device at 100C or even 50C on the back of a chip with lots of pins or a temperature sensitive analog circuit.

The other thing you need to be careful of with backside components is the silk-screen. If you use one on the back make sure it does not interfere with any vias, solder points, or test pads.