EKG/ECG are only able to detect and monitor heart rhythms
in real-time. That means that if you have an irregular heart rhythm it would have to be present at the time of the monitor to be detected. Most irregular heart beats are sporadic and un predictable i.e Tachycardia's (heart rate over 100 beats per minute) they may come on during a rested state and continue for minutes or in some cases, hours. If this happens to you don't panic, for some people this is normal and harmless BUT DON'T IGNORE THIS EITHER.... seek medical attention if you experience any irregularities. Make sure you are 100% honest with your doctor so you can be properly treated. Anyway, to finally answer your question specifically, yes. There are lots of different problems that can occur within the cardiovascular system, some can be quit benign and some can be very dangerous. To properly identify the problem you need to get the proper tests done. Once again, be sure that you are very direct and specific when describing your symptons. That is all.

(this is just my oppion. I am not a doctor or claim to be. I just have experience in the medical field from the Fire/Rescue first responder side of things.)