(Image from guidobass)
Below is a list of things to keep in mind whenever Mission is on the board. This is not meant to have deep analysis about the event but rather just things to keep in mind when it shows up. Additionally, whatever feedback is left about this write-up will be incorporated into the article so that, hopefully, it can be a collection of ideas from the community rather than just one person. Without further ado, here is the list (in no particular order of importance).
• Gaining – This is the first thing that jumped out to me when reading the text of Mission. If I can’t buy things, I will just gain them instead. Even if the Mission turn is used just to use Workshop for a Herald, say, I feel like it is worth it do so because it also cycles you (which is usually good while building the deck). Other notable gainers include Horn of Plenty, Procession, Graverobber, Artificer, University and Artisan (more exist but this is off the top of my head).
• Trashing – It might be worth it to spend that 4 coin to go looking for Steward, Junk Dealer or Chapel. Also in this section are the cards that trash for benefit like Upgrade, Governor and Forge. Also, see Dingan's idea down below.
• VP tokens – You can get Monument down or play Bishop a second time. Empires also includes Gathering piles so you can either sweeten the pot or clear the pile (e.g. Farmer’s Market) on the Mission turn.
• Attacking – On the Mission turn, you find attacks that have not shown up yet but you think would be quite important to get in like Militia or Ghost Ship (for that constant pressure), say. Naturally, there are some attacks that have no effect the second time (like those aforementioned). However, there are some that do hit twice. The most notable of those are the junkers (e.g. Young Witch, Cultist, Familiar, Torturer (by Jimmmmm)) and the trashers (e.g. Knights). Also included here is Mission’s ability to evade hand-size attacks; you get another turn but with 5 cards this time (though you forgo buying). Additionally, only one copy of duration attacks is needed to keep your opponent under constant pressure since you can potentially replay that same copy during the Mission turn. Included here is Possession.
• Duration cards – Nearly every duration card can benefit from a Mission turn (Outpost may be the only exception). You can use your Mission turn to set up Wharves, Caravans, Archives and, most notably perhaps, Tactician so that you can reap the rewards on the next turn.
• Buy events – This comes along with the expansion that introduced Mission. Whenever there is another event with Mission on board, this something to keep in mind. Alms is an excellent partner for Mission for instance. Also, the usual one-time buy events like Inheritance and Pathfinding can be bought on your Mission so that you can use the first turn to buy cards.
• Travellers – You can upgrade your Travellers on your Mission turn allowing for a faster turnover. Notably, you can either call or set aside your Teacher on the Mission turn allowing you to get a full cycle from Teacher in just one turn potentially. Speaking of Teacher…
• Tavern mat – Cards can be called from the Tavern (Transmogrify, Wine Merchant, Teacher) or set aside (Guide, Transmogrify) during Missions.
• Coin tokens – Laying down Baker or Candlestick Maker a second time is obviously good. Butcher, as always, is great gaining tokens and gaining potentially.
• Debt – Pay off your debt if the occasion presents itself
• Set-up (from DG) - Mission can help to set up your turn to be a good one. You can rid yourself of the Haunted Woods attack or use something like Apothecary, Scouting Party or Cartographer to top-deck good cards (and potentially remove worse cards).
A natural comparison to make is with Outpost since Outpost turns can do all of the above things. In fact, in the late game of an engine, Outpost will often out-class Mission. However, Mission’s main advantage (outside of not using an Action or a deck slot) is that it is always there. For example, you may want an extra turn to gain the first Prize but won’t usually have an Outpost there to get you there. You want to use Transmogrify or Rebuild to close out the game but won’t have Outpost in deck because it doesn’t fit well; Mission can get you there. You may want to play Young Witch a second time especially since there is no bane in the way; Mission. These examples also highlight another advantage of Mission: the extra 2 cards (useful with Governors also, for example).
However, the main point is that it is there whenever you want it (and have the money). This can be useful particularly in the mid-game where Outpost isn’t usually seen.
Another point worth consideration is that Mission potentially involves not buying cards on both turns not just the one. If you buy Mission, you are saying that it is more useful to have potentially two turns not buying cards (or one turn not buying as many cards) than it is to buy cards for the one turn. Knowing when this is useful can guide you on purchasing Mission. (from Chris is me)