Here are ten things I would have done differently from the start:
1) Personnel, ships, and equipment should have had a cost system. Jean-Luc Picard is already objectively better than Benjamin Maxwell, the fact that they were equally expensive in terms of cost to draw and cost to play was bonkers at the time (really just a justification to make players pay more cash for the better cards). This was something 2nd Edition really got right.
2) Nouns and Verbs should play differently from one another, and probably have separate decks. This would have prevented the vast majority of verbs from having become unplayable binder fodder and yielded a much more interesting and varied game. I'd probably have two separate decks and the ability to draw from either one into your hand (perhaps your draws must be evenly split?), and your normal noun card play would be distinct from your normal verb card play (so you're incentivized to use both, instead of almost every card play being a noun).
3) I agree with Takket, dilemmas should have costs. Something a lot closer to 2nd Edition - using fixed dilemma combos is boring, incentivizes seeing the same sorts of dilemmas over and over, and results in most of a player's time investment being in the deck prep, rather than actually playing the game. Am I the only one who things dilemma combo crafting is by far the most tedious and time-intensive part of deck building?
4) Seeding for free should have explicitly been a thing (just like playing for free), instead of later being selectively applied to sites and missions.
5) Much more deck manipulation should have been incorporated into the game from the beginning. The game started out too slow, with draw-one-play-one gameplay. The "hack" to fix this was adding downloading, free plays, and dial-a-skill abilities, but that only selectively accelerated portions of the game, leaving significant other portions now unplayable. Perhaps this would be less of a problem if #2 had been implemented.
Relatedly, the game is a card game, and really should lean into that, using mechanics that are unique to cards and decks. Star Wars CCG had a really lovely design, where the cards weren't just the components of the board and the pieces of the board (like in Star Trek CCG), but they were also both the life counters (your remaining draw deck) and your currency (your Force pile). I'm not saying Star Trek CCG should use the same model, but a truly elegant game really uses its specific medium (the CCG, in this case) to create an experience that couldn't be replicated in any other medium. Does Star Trek CCG really do that?
I think 2nd Edition does this to some extent, but it also strays too far from the "Trek Simulator" that 1st Edition was. I'd like the best of both worlds.
6) Cards should have been restricted in quantity within a deck, unless that card specifically calls itself out as an exception. That way you don't end up with Q-bypass as a near-instant win strategy, for example. Takket also mentioned this as a possibility for dilemmas, but I think the same might need to have applied to draw deck cards as well. So I envision cards like Rogue Borg Mercenaries calling itself out as an exception (since their original design intent was to act as a swarm, rather than as a ping card), but I'm not sure Loss of Orbital Stability was meant to be a super-spammed ping card, and since it's not a swarm card, it should have been limited.
7) Voyager should have been a completely separate game. It was crowbarred in to the design of Star Trek CCG, even though it pretty much takes place on a different board, which severely limits interaction. It's also why two of the Voyager affiliations really shouldn't qualify as affiliations, as they aren't competitive, diverse enough, or interesting from a fan perspective - but the crowbarred design mandated that new affiliations be added to pair against the Voyager affiliation.
Imagine chess was a game with expansions, with two players bringing their pieces and fighting on a board. Then the "Voyager Chess" expansion allows players to bring their own board with their pieces...so now you're playing on separate boards, basically playing solitaire (unless the other player also brought the expansion board to play on instead of the normal board).
In other words, Voyager should have been to Star Trek CCG what Young Jedi was to Star Wars CCG. Inspired by some of the mechanics, but a wholly separate, incompatible game (although I wouldn't make it juvenile and simpler, the way Young Jedi deliberately was).
By the same token, mirror quadrant and gamma quadrant missions should have remained limited in quantity, to force players to come play on the "main board" of the alpha quadrant. Decipher was largely smart about that.
9) Similarly, TOS, Enterprise, and movie era cards should have been limited in quantity so that they can be "splashed" in to decks as alternate-universe guest stars, rather than being the sole focus of your deck. It doesn't make sense that in a game set in the 24th century, you can roam around with an all-23rd century crew. Your skills and technology are a century out of date, you shouldn't be able to compete. A measly Klingon Bird-of-Prey should be able to easily fly twice as fast and then one-shot you.
Or if you want to have an all-movie era bridge crew roaming the spaceline in a time warp solving missions on behalf of the Federation, fine, but then you accept it will never be able to compete against modern 24th-century decks.
10) Affiliation flavor should have been significantly greater and more diverse, with much deeper mechanical differences. The Borg, and the way they feel and play differently, is a perfect example, but nothing else lived up to that difference. For instance, the Ferengi should really have leaned into the idea of heavy borrowing and investing for massive payoffs. I'm imagining cards that cost Ferengi significant points (like a total of 50 or more points), in exchange for a lot of power that they can use to recoup those costs and profit from (in other words, giving them the ability to blast through multiple missions, which they'd have to do to make up for the heavy cost of the "loan." Other affiliations can get three missions for a win with 100 points, but Ferengi might need to get five missions because they need to get 150 to pay for their 50 point upfront cost). Cards like "Recruit Mercenaries" tried this, but they were far too weak for their benefit (the true cost of "Recruit Mercenaries" being the card play, rather than the -7 points - but again, that gets solved somewhat with #2, above). Cardassians had Nor mining, to give them mechanical advantages with "mining" their deck, but it was hard to set up, required significant infrastructure, provided minimal returns, and then got nerfed.
Again, another thing 2nd Edition may have gotten more right.
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I don't understand the obsession with splitting up affiliations into factions. The CCG was always a Trek universe simulator, and Sisko would have had no problem working with Data. I also dislike the narrow focus that factionalization introduces, as it makes decks build themselves.
And I dislike that it's used to justify "powering up" what would otherwise be weaker factions. For instance, maybe mirror factions should be weaker! They weren't a sustainable society and can't compete with the Federation or Klingon Empire in terms of manpower, quality, or achievements. That's why they should be splashed in for fun, flavor, and skill gaps, rather than being the focus of an entire deck that stands toe-to-toe with the best of one of the major alpha quadrant powers.
Do the Klingons get a "new toy" if there's a great new Klingon card and no faction restrictions? Sure, but that's part of the fun! That's what expansions are for in the first place! Why shouldn't the existing factions get new toys to play with, instead of constantly making new factions to get their own toys?