If it is a small bore and has the tappet covers on the rear of the engine those gaskets leak and drip down the back of the block, sometimes it is leaking because the bolts have loosened off and tightening them up may cure it but the cork gaskets go hard over time so replacement may be necessary.

wash down the engine with detergent and then run the engine.  Oil like everything else is subject to gravity. Start at the valve cover and look for your oil leak(s).    From your pic, it looks like it's the shifter seal. Pretty easy to replace if you get the car up in the air so you can get under it.

Yep = pumping then loss= Most likely Clutch Master= But the slave is also pretty Cheap and part of the styem .
   Go ahead and replace all 3 items and youll be back in business.

Clutch Master
 Clutch Slave
  Rubber flex hose.

Pumping the clutch did work for a while but no longer. Very little resistance when depressing the clutch. I'm going to bring it in to a mini specialist and get this fixed. I need to get it to the DMV for inspection and registration. 

Thanks for the response. Appreciate it.

When it 'grinds' and wont go into gear.. can you rapidly pump the clutch and get it to go into gear?

 That is a sign of a leaking clutch system.  your pumping makes enough temporary pressure to work, but it looses it and wont engage.

Typical for the Clutch Slave Cylnder to fail and cause this.  Next would be the Clutch Master Cylnder.
   Replace the rubber flex line while doing the job on the Slave CYL. too.

Thanks for the quick responses everyone. This was my first question but certainly it won't be my last. It has a clutch issue - will not go into first or reverse sometimes, just grinds and makes a very unpleasant noise. Just one of many things that will get me out of the house and keep me busy.

I should have mentioned that it has a 998 A+.

Thanks again.

With mini rubber parts being crap, I would let sleeping dogs lie. I would routinely replace good old rubber if it was still good only to have the new rubber disintegrate.

Seeing the very clean streak on the CV Housing = under the CV Joint.. the others  /we agree the CV axle seal is leaking.

Drain oil
Pull out Axle from car.

the quick and easy fix is to pry out the axle seal = Install new.

But while in there= consider like mentoned. Shift shaft seal kit too _ perhaps also replacing the  differential output gasket too

https://www.minimania.com/part/22A1611/Differential-Side-Cover-Gasket-For-All-Mini-Mini-Cooper-S

https://www.minimania.com/part/ADU5738/Classic-Austin-Mini-Cooper-Differential-Side-Cover-Seal-yoke--Pot-rod-Change

https://www.minimania.com/part/AHU1672/Classic-Austin-Mini-Cooper-Rod-Change-Shift-Seal

Probably want to consider BOTH sides of axles seals = if one is tired. the other will closely follow.

Judging by the surrounding dirt and the location of the fresh drips, including the one on the exhaust pipe bracket, the leak is probably farther up. If it were only the rod seal, the drips would not form in those locations.

Assuming (from the rod-change gearbox) that the engine is a later model that does not have tappet covers, the first place I'd check is the rocker cover gasket. Your engine is probably mucky from there down.

Fortunately, being on top of the engine, it is an easy item to check and replace. When you do, be very careful not to over-tighten the hold-down bolts. The gasket only needs enough pressure to hold its surfaces against the head and rocker cover until the sealant you use sets. Over-tightening distorts the gasket and it would leak, probably worse.

Looks like the differential seal may be leaking and would need to be replaced. It would be too easy to just replace the rod shifter seal.

These help, somewhat. 
https://www.minimania.com/part/MSSK050/Classic-Austin-Mini-Rod-Change-Anti-Oil-Leak-And-Seal-Kit

I found you need to clean everything really well to identify where the other leaks are coming from.

I just took ownership of an 81 mini pickup and it's leaking quite a bit. Hoping someone on here can advise on where to start identifying the source and fixing it. I've attached a couple of pictures.  Thanks!