Things aren't very rosy. The targeted date has been (up until today Monday May 8) 24 June (with no earlier than 19 June launch). The actual date is dependant upon the Spektr launch (and its impact on the EVA's and activity needed to juggle the modules prior to the STS mission).
Each days delay puts the launch back some 24 minutes or so in order that Mir's orbital plane can be intercepted (I figure a 19 June launch at 2243 UTC will will translate to about 2045 UTC by 24 June). Thus the launch times occur nearer to sunset with each passing day, and the number of viewable passes during the mission is reduced. For 24 June the shuttle would be best seen around central Europe; passes would be visible up to about mission day 7, whilst in NW Europe only a handful of low elevation passes for the first (approx.) 4 days would be viewable and the ascent pass would occur only a few minutes after sunset. If Spektr arrives at Mir on time, NASA may exercise an option to shorten STS-70 (from 7 to 5 days); maybe they can realistically aim for the 19 June date then? If so the viewing improves substantially.
The 'upside' to a delay is the increased 'viewability' of the STS and ET during ascent. As the days pass the launch time is earlier, the pass closer to sunset and so the Earth's shadow height at the observer's location lower resulting in a potentially longer illumination time for the orbiter and ET (They look like being visible for a short time during a 19 June launch for observers in Western Europe).
These are of course constrained by local sunset - beyond (approx.) the end of June virtually all passes would be lost in the sunset and the early evening daylight.
Incidentally Mir's evening apparitions will begin around 8 June but will have died off by around 25 June.
Apologies to all non-European readers for my indulging in this regionalised description; though a similar argument applies to N. Amercian viwers on the East coast as regards viewing the powered ascent during the night [and passes during the mission for those in more Northerly American locations].
Here is the current preliminary element set :
1 99971U 95173.92712729 .00020693 17897-8 46542-4 0 18 2 99971 51.6695 129.4019 0041116 0.0672 190.4988 15.95310275 11