This venerable and creaking space antique is due to be sent crashing back to Earth in March 2001, now that financial backing to turn it into a space hotel has fallen through. The latest prediction is re-entry on 20th March if the Russians can bring it back in a controlled fashion.
Apart from a tendency to get lost now and again, there is no reason why Mir cannot be predicted accurately as it is a large, easily visible object, in fact slightly larger than the International Space Station currently is. It's orbital inclination of 51.4 degrees is slightly greater than that of the ISS, though it has a slightly lower orbit (170 vs 205 miles), so the characteristics of the ISS sightings also hold reasonably true for Mir.
Since the beginning of 2001 Mir's orbit has been decaying due to atmospheric drag and the lack of any reboosts to raise the orbit. Normally it orbits at an average height of 340km but by early March 2000 this had declined to 250km, with a drop of about 1.5 km a day. As the altitude drops so the amount of drag increases, but because the drag also depends on the density of the upper atmosphere, which is governed by the activity of the sun, we cannot yet be sure exactly when re-entry will happen. On current estimates 28 Mar 2000 looks to be the likely day of an uncontrolled re-entry.
However, the plan is to de-orbit Mir in a controlled manner using a Progress supply craft, so that it comes down over the South Pacific. For this, the controllers are planning on 20th March.
The re-entry should be a spectacular sight as 130 tonnes of space station meets a fiery end in the upper atmosphere, and some 20 tonnes of material is expected to reach the ground intact. The Russians have had in the past a good record of bringing down unwanted, albeit smaller, Salyut space stations into the Pacific so there will probably not be a lot to see from the UK. However, if anything goes wrong potentially anywhere on Earth between latitudes 52 degrees N and S is in the target zone, so a watchful eye on the heavens and a hard hat to hand could be a useful strategy!
For more information look at Space Science, which also has a link to J-Pass, a real-time calculator to predict the visibility of particular satellites from any given location. In the weeks and days leading up to Mir's demise it looks as if it may not be visible again from the UK as none of its overpasses fall within the conditions necessary to observe a satellite, i.e. darkness on the ground but sunshine at the satellite's altitude. If still aloft, it potentially starts to become visible in the mornings before dawn from the end of March (starting on 28 Mar at 0614 - 0621 GMT), so it might then be possible to catch it on what could be its very last day. However, at this time the sun will already be up, so unless it is actually re-entering and burning up (in which case it will probably be visible in daylight anyway) it will not be seen.
The Russian controllers executed a text-book re-entry procedure that sent Mir into the south Pacific, the graveyard for many previous items of unwanted space hardware. Residents of Fiji got a fine view of the fireball as it passed overhead, but the rest of the world was spared any danger of falling debris.
Full story at Space Science.
At the time of writing this (13th Jan) I have seen Mir twice from Hurst Green in accordance with predictions. Compared to the ISS it seems to be of similar brightness but moves more quickly across the sky (on account of its orbit being lower) - you get about 5 minutes of useful visibility on a high pass compared to perhaps 7 minutes with the ISS.
On the evening of 6 Jan 2001 it rose almost due west, though I did not spot it until it was at about 20 degrees altitude, and it passed slightly to the north of the zenith, reaching a maximum brightness of about -1.5 (not quite as bright as Jupiter). It passed into the Earth's shadow at 5.54pm while still at a high elevation, taking about 10 seconds to fade from sight.
On the second appearance, on the evening of 13th Jan, Mir passed much further south, rising again in the west but reaching an elevation of only about 45 degrees before descending into the SE. Being further away it was not expected to be as bright as before, and at its highest point it reached about magnitude +0.5, about the same as Saturn. However, as it moved away it initially began to fade but after a minute it began to increase in brightness and reached about -1.5 before fading again. The episode took about 30 seconds and was probably caused by sunlight reflecting off the flat solar panels. This phenomenon is well observed in Iridium satellites and could be well worth watching out for given that Mir is may times the size of an Iridium satellite.