I have the July 17 WIP of ZSNESW, though the problem is in older builds as well.
Procedure:
Start the game, get past the opening text exposition; you should be at a screen saying "COMMUNICATIONS". Press left twice and you should be at a screen saying "ENGINEERING". Press the A button. Now select either "Weapons", "Shields", or "Engines", and press the A button again. Whichever one you pick, you'll see a bunch of textual garbage on the screen, typically a bunch of zeroes or "PPPPPPPP" (etc.) Sometimes the game might crash the emulator (that is, ZSNESW will abruptly exit) upon trying to enter these screens, which is unfortunate since they are essential to gameplay. (Note: I have not verified the crash problem with the latest WIP, but as the text problem exists, the crash likely does, too.)
Here's the ROM info from Snes9x (which does run the game correctly):
File: Q:\ROMs\SNES\Star Trek - The Next Generation - Future's Past (U).zip
Name: stng
Speed: 30/FastROM
ROM Map: LoROM
Type: 00
Kart contents: ROM only
Header ROM Size: 16Mbits
Calculated ROM Size: 16 Mbits
SRAM size: 0KB (0Kbit)
Actual Checksum: DC9A
Header Checksum: DC9A
Header Checksum Compliment: 2365
Output: NTSC 60Hz
CRC32: 8DE80428
Licensee: Spectrum Holobyte
ROM Version: 1.0
Region: USA/Canada
Star Trek: The Next Generation bug
Moderator: ZSNES Mods
Star Trek: The Next Generation bug
[url=http://gameinfo.wikicities.com]gameinfo wiki[/url] - Like GameFAQs, but [size=50]it will eventually be[/size] better
Yep I confirm that this is happening but I can't say if this bug was a bug in the original cartridge or not.
It shows this at the bottom of respective sections.
Shields: 00000000000000000, etc.
Weapons: 000000000000/ number of photons: 25000000000, etc.
Engines: AAAAAAAAAAAAAAAAAAAAAAAAAAPPPPPPPPPPPPPPPPPPPP, etc.
It hasn't crashed on me but I do see this "errorenous" data.
I have the same dump and it is considered a Verified Good dump.
It shows this at the bottom of respective sections.
Shields: 00000000000000000, etc.
Weapons: 000000000000/ number of photons: 25000000000, etc.
Engines: AAAAAAAAAAAAAAAAAAAAAAAAAAPPPPPPPPPPPPPPPPPPPP, etc.
It hasn't crashed on me but I do see this "errorenous" data.
I have the same dump and it is considered a Verified Good dump.
That the problem doesn't show up in Snes9x at all suggests that it should work, and it almost certainly doesn't occur in the original cartridge. Moreover, the cart certainly shouldn't crash the emulator no matter what happens. You won't see smoke coming from your SNES because of an illegal instruction or something. 
Yes, NSRT thinks it's a good dump.
- Kef

Yes, NSRT thinks it's a good dump.
- Kef
[url=http://gameinfo.wikicities.com]gameinfo wiki[/url] - Like GameFAQs, but [size=50]it will eventually be[/size] better