Have you ever noticed a discrepancy in blood pressure monitors readings?

Yes, there is a great difference in blood pressure readings, for many reasons, some of which are mentioned above. Calibration, standing/sitting, obesity using too small a cuff, user ERROR.
If you consistently get an inaccurate reading, notated on your medical record showing a non-existent high blood presure reading, you will find yourself being treated for hypertension, with meds that you don't need! Additionally, this error can lead to denial of insurance, or higher rates.

My doctor regularly takes my bp 3 or 4 times in the course of a visit, because the reading are often quite different.

Blood pressure readings vary due to what you've been doing just before taking it. I read that the best time to take it was in the morning? And if they took the bp on my left arm, it's different from my right arm. Sometimes, they can't hear anything on the adult bp machine and think it's broken. So they go and get another one or the one for children.

If you have BPM at home, if you get a reading at a daily set schedule, you can bring your notes with you to the doctor's office. This way, the doctor can compare your daily readings with the one at the office.

Well, I don't have a practice, but I've noticed discrepancies among meters. I've also noticed fairly large differences using the same meter, since bp can change fairly quickly.

One thing we did was take our bp meter to the doctor with us once. He checked them to make sure he was getting the same readings that he got in his office using his stethoscope. It turned out our meters were pretty good.