Expect problems, be smug if you don't get any.
I've had 6 morgans, 2 new. They all have issues. Don't expect the build quality of mainstream manufacturers.
DO NOT BUY INTO THE HAND MADE B*LL*CKS!!!!!!!
In the interests of balance I should say that I have also owned two Morgans from new, both 4/4s. The first was purchased in 1992 and gave me over 20 years of trouble free motoring - it was my daily transport. There were no issues with the car during this period. Likewise, my current 4/4 purchased in 2013 has also - touch wood - been trouble free.