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On my Cooper S I used a black indelible marker and placed a solid mark between the low and high ranges.You can now see the oil and level. Sorry to hear about the problem, but would take it back and have them drain the excess. It will damage your engine because it stresses the oil seals (pan, valve cover, etc.) and places and undue strain on the oil pump too. Any way, hope the black marker suggestion helps others out...
This is why we need an oil pressure gauge on our mins.
Flav, did you call the dealer and report the mishap? You could also call the mini roadside assistance, and have car towed to dealer if you are super concerned.
-- If you have to rely on an "oil pressure guage" as an indicator of your oil level,you are in trouble. there is plenty of leeway in the upper and lower marks on that stick. It is just a rough indicator of the oil level. remember there is almost 5 qts in that sump.