Found after letting my car sit for three days and not changing the oil since February when it is now August that the car would lug between 1 - 3k rpm and 10 - 25 mph in second gear. This was not the issue earlier this year. I changed the oil - I hadn't done so for not good enough reasons. It was 16K miles past due. The engine will idle fine enough when sitting still, but after driving in traffic I get scared to stop because going from 0 - 10 in first gear leads to a TON of lagging and lugging - mild and unpredictable loss of power followed by jerking the car because of the regaining of power. Here are the facts:

After oil change and before 10 miles on new oil
I noticed that my ignition wires are rubbing raw down to the white on the 4 cable and the 3 cable has some wear where the 3 cable is resting on top of the 4 cable slightly at a soft bend.
I'll check the air filter after this post.
The lugging went away but came back after about 5 miles of driving around and gets worse the worse it is being driven.
Specifically I noticed in second gear the car lugged between 11 - 25 mph between 1500 - 3000 RPM where this was not happening earlier in the year.
in first gear the car lugged after warming up to complete operating temperature at 3pm with the weather around 88 degrees Fahrenheit. The lugging would happen from 0mph dead stop at a light to 7mph and the engine would idle very rough during the stop.
the lugging is aggressive and caused my Traction control light to come on. Perhaps this is electrical or the engine simply got close to dying.

As an update I found that the air filter housing has screws that have wobbled/worn the plastic threads they were in to nothing. So the air it's been sucking it has been unfiltered as my filter is basically spotless.

EDIT2: My car was having these issues of lugging and coughing at me when warmed up before i replaced the oil. Now that i've done some research I think that it's the coil pack at 200,000 miles that is burnt out. I'll go to pick n pull to get a new one later this week. I will update more if i do not get more help.

After getting home and parking the car I noticed the engine had a rough idle until i turned it off and turned it back on.
When turning the car back on the engine would initially run up to 1200 - 1500 rpm then slide down to 500 then level out around 800. The 1200 seems fine, but it almost dies when it slides back down, and when the cooling fan came on the idles dropped to about 500 too and the engine shook.

5 speed
04 R50
Naturally Aspirated

 

Your irregular idle is a classic symptom of a vacuum leak. Start there.

 

I thought the same, but the issue gets worse as the car warms up, and my cables from the ignition coil are irregularly worn down causing an increase in voltage and heat which causes misfires

 

Why don't you change the spark plugs, wires and spray contact cleaner on the plug in back of the coil. In other words, bring the ignition system back up to a new level. This is not to say, this is the whole problem, but it sounds like you have neglected to maintain your R50.
The air filter should be changed, as you have stated. It would not hurt to put some Dry Gas additive with injector cleaner in it, to the fuel tank, as sitting can cause moisture and put crap from the tank in the injectors.
Get an OBD II test done, so you will have a better idea how the health in the electronics is doing.and let us know of any codes the system has stored.
Bring this conversation to the gen 1 area, to get more direct help from others that share your model.
Show us some pics of your Mini too!

 

Replaced wires and wiped off nodes. I’ll get a garage in November so I’ll be free to work on my car. The new wires did the trick and my car runs fairly smooth. Here soon I’ll take apart the engine and replace all seals and clean everything off replace the timing chain and the timing chain tensioner. Seems like I’ll clean my gas tank too and switch to premium fuel.

thanks guys!!

 

If the spark plugs have not been replaced in a long time. Replace them with NGK brand spark plugs. It will make a big difference on how your engine runs. It will increase fuel mileage too!