Push pull core saturation
Push-Pull converter is one of the oldest topologies around, so it's hard to even think about how many are out there working. It's true though, a side to side imbalance can cause the core to walk into saturation. How do people keep this from happening? 

Well, here are some things to do (and not to do) to keep the core balanced: 


Absolutely do not use a core that has a square BH loop. These have extremely high \$\mu\$ and will quickly end up saturated. 
Use a ferrite core. Something like and EE, or EP, or Pot core. 
Gap the core. Sometimes just putting the two core halves together can be enough of a gap, but not usually. Expect to have need of some kind of added gap. The gap linearizes and stretches out the H of the BH curve allowing it to take more coercive force (H). That's another way of saying the gap allows the core to take some DC bias. Also it will minimize the variation of \$\mu\$ found in ferrite, which can easily be +/-20%. Now, a gapped core will have higher magnetizing current, so loss will be a little higher. But, by tayloring the gap to your needs, a highly efficient power supply is still possible. Also, if FETs are used as switches, as an imbalance of magnetizing current occurs, the FET exposed to the higher current will warm up, raising \$R_\text{ds-on}\$ of that FET and causing currents to rebalance. 


Here's an article that talks about voltage mode control and Push-Pull converters "Voltage Mode Converters Deserve a Second Look".

You could also use current mode control, which uses the feedback loop to keep currents in balance.