Here is a list of some of the differences worth considering when designing or troubleshooting (pin differences are outlined in the sections below this list):
The Digispark is powered by an Atmel Attiny85 MCU - this has many differences from an Arduino's ATmega328 and some libraries may not work correctly on it.
The Digispark only has about 6 KB of flash memory for storing your code.
Pin 3 and Pin 4 (P3 and P4) are used for USB communication and programming, while you can use them in your circuit if you are not using USB communication, you may have to unplug your circuit during programming if the circuit would impede the pin states or dramatically affect the voltage levels on these pins.
Pin 3 (P3) has a 1.5 kΩ pull-up resistor attached to it which is required for when P3 and P4 are used for USB communication (including programming). Your design may need to take into account that you'd have to overpower this to pull this pin low.
The Digispark does not have a hardware serial port nor a hardware serial to USB converter. An example library (DigiUSB) is provided, as well as some example code and a serial monitor like program, but communication with the computer will not always be plug and play, especially when other libraries are involved.