Increase Microcontroller frequency and Speed
Which area?  Everywhere.  Anything involving external interfaces -- button input debouncing, ADC or SPI rates and delays, RAM or flash acess times, LCD refresh circuits, etc.  Anything involving delay loops, interrupt timing, external flash or ADC delays, etc.  And even lots of things you might not expect, like race conditions between isolated pieces of code because something finishes faster than it used to and some time-based event didn't expect it to have updated a variable already. 

Of course, this is highly dependent on what your code actually does.  If it's all math, you may need to change very little.  But most microcontrollers are used to interact with the real world in many ways.  And the real world won't change speed to match!