I’m not sure, it looks alright apart from the nylon ends...

 

Is it leaking anything?

 

No, nothing that I can see...

 

I think it should be ok if it's not leaking anything.

Not sure if the nylon string is normal on an engine mount.

 

What year MCS is this...?

When this mount is compromised in an 2002-2004 model driver will hear ( loud ) clunking from area of right side of car ( behind glove box on US models/left hand drive ) when going on/off the throttle.

These earlier mounts are not hydraulic, thus will not leak like those in 05/06 face lift models....

 

These are indeed filled with fluid. They will not usually leak, but the fluid can "disappear". That one looks like it has shrunk down a bit.

 

As MINI33342 stated, the old-style rubber/nylon strap mounts are fluid filled too.

Don't worry about the nylon ends. All in all, yours is not the worst I've seen...
It does appear to bulge a bit at the bottom and just above the nylon strap, which is indicative of it slowly wearing out.

They can burst when they fail and make a bit of a mess, leaking hydraulic fluid underneath.

I replaced mine back in November of 2017; Here it is today.

 

Wow, by comparison mine is “smushed!” Since mini is a 2003 (made 12/02) with 65k miles it’s probably time for all 3 new engine mounts. I’ve heard that the solid ones are too rigid and expensive, but what do you think about this set?
https://rover.ebay.com/rover/0/0/0?m...2F352357509042

I figure as long as they’re new rubber...

 

The set on eBay looks to be the proper OE style mounts. I'd suggest you replace with original style mounts.
I noticed a huge difference as new mounts absorbed engine vibrations, translating into smooth idling and elimination of most rattles in the cockpit.

Unless you're racing the car and want to stiffen up everything, I would not suggest aftermarket/polyurethane mounts, as they will amplify everything the OE mounts eliminate.

 

By the way, what’s the reason a 2003 MCS can’t retrofit the engine mounts from the

2004-2006?

 

There's a different engine mount bracket on the post-facelift cars which eliminated the secondary upper mount that's in the package you linked on eBay.
Just fewer parts and simplification of the system (probably per the bean-counters); not sure it made much of a difference performance-wise.

As to retrofitting, nothing would line up, as the holes in the chassis aren't there on the pre-facelift vehicles.