Yes

Torn diaphragm??? What kind of carb do you have? Check it for air leaks.

To my thinking a race engine with a cam designed for full throttle is "lumpy" at idle. Is that what you mean? 

Maybe the carb just needs rebuilt? Would a torn diaphram cause it to idle like this? Old fuel maybe?

Like a car with a racing cam in it at idle. Runs great and plugs are a nice shade of brown. Not white (lean) or black (rich). No lag or stumble. Maybe they did put in a different cam? On to another delight. Changing the speedo cable. Can get down there and reach the knurled end but it's not hand tight. Almost impossible to get a tool down there holding it. I had the idea of a sink basin wrench to turn it but the firewall is in the way with its angle.

Jan:

What do you mean by "lopes"?
Do you mean the engine rpm rises and falls when at idle or does it surge under load/power?

An undulating idle suggests an excessively lean idle mixture: the engine lags/stumbles due to insufficient fuel, then picks up again when the fuel supply matches the low rpm, and the cycle repeats. If the PP put in a different cam and did not install an appropriate carb mixture needle (assuming you have a SU carb), then he might have tuned it for the best power but the needle does not provide enough fuel at idle. Note: there are hundreds of types of needles!

The unconnected vacuum advance is not an issue, unless the port on the carb has not been properly capped. That would result in an air "leak" producing the lean idle problem, if that's what you have.

It is not critical at the dizzy end - a vacuum advance is a fuel economy device: it provides advanced timing at idle, permitting a leaner (but not too lean!) idle mixture to save fuel. As you open the throttle the vacuum reduces, along with the advance. However, as rpms increase the cetrifugal mechanical advance takes over, providing the correct amount of advance for the rpms.

A worn clutch would either grab, making engagement difficult or slip in high gear going uphill, and eventually worse affecting lower gears. As Kermy suggests, a high pedal could be poor adjustment or worn linkage or both.

A 1987 Mini would likely have an A+ with a Verto clutch = no adjustment in the arm. However the arm and clutch release plunger should be checked for excessive wear and play, and the stop-nut on the plunger should be checked for proper adjustment.

I'd try adjusting the clutch before replacing it.

     87 carbed Mini runs but lopes. PO said it has a different cam in it? I doubt that since the clutch is on it's last leg engaging near the top. If you did engine work why not a new clutch. Dizzy has a vacuum advance but not hooked to a vacuum source. I do all my own work on my cars and bikes but would like another opinion before I start digging. Anyone in the Pittsburgh area want to take a look? I'm in Lower Burrell. Thanks!