Arduino ECG/EKG Heart Rate Monitor

don't worry too much about the risk of shock from a ground lead that is not isolated. It is really quite hard to electrocute someone. That being said it is pretty easy today to make a fully isolated instrumentation amp. We were doing that 40 years ago and even then it wasn't impossibly hard. It is worthwhile to use ultra low noise op-amps and keep everything running on a few coin cells for absolute safety. The simplest safety system is to use a wireless connection as some of the forum have suggested. If you go to EEG signals then the noise becomes very important as the signals are 1/10 of the ECG ones.