My Dominion username is ScreamingHippo as well.
To start, a few things that aren't on the list of your specific questions:
I would like the ability to replay with the same setup of kingdom cards as last game. The use case is when playing against the AI and your strategy did not work and you want to try a different one.
I would like the ability to always exclude certain cards from a game against the AI. For example, games with chapel can get repetitive after a while, so I'd prefer to play without it.
When playing against another person, I'd like a better indication of how our rankings changed as a result of the match and why.
1. An offline client, allowing you to play campaigns against bots
Eh, an offline client isn't a big deal for me and a campaign is not a high priority either. I played the MF campaigns, and I did like that they introduced the card for each expansion at a set rate, but they were too long and Dominion doesn't seem to lend itself to a particularly good story. I wonder if some kind of 'challenges' - games against an AI, potentially with altered rules, a specific setup of cards, etc. with no attempt at story would be better.
2. A bot with a setting for different play styles
This would be more interesting in games with more players, but I generally play 2 player against the AI so...
3. A strong bot.
A strong bot would be good. I like to play against the AI sometimes because then I don't need to worry about being interrupted and I would like an AI that can handle different setups well.
4. Options for timed games
Not a huge deal, but it would be good to have
5. Options for undo settings
I would really like a better undo function. Perhaps a little undo button next to steps in the log where I could choose to go directly back to that step. Another response I happened to see described an idea where you could setup at the beginning of a game an undo policy, where you don't have to respond to every undo request, but you could set a policy about what types of actions you would allow an opponent to undo.
6. Online mini-tournaments; the option to easily create one for you & your friends.
I'm not sure I would use this feature, but it sounds like it could be fun.
7. Option to invite specific players to your table
Definitely need this! Some better searching and messaging for people would be good too.
8. More translations (to what language?)
Klingon? Just kidding. I don't need it in another language, but I'd love for people around the world to be able to play.
9. Better animations when cards are gained/bought/played/...
I don't care about animations very much.
10. Better visualization of split piles, Archive/Crypt contents, Prince targets, ...
Yes, please. And better visualization of duration cards in play would be good too.
10. Option to hide the log
This might be a good for a mobile version, but on a PC I think I'd keep the log up - particularly if the undo function is based in the log, which I think it should be.
11. Android app (or just improved compatibility?)
I might use that. I don't particularly care about app vs. improved browser compatibility
12. iPhone app (or just improved compatibility?)
I have an iPad, so I might use that as well, but I have lots of other games on it, so maybe not.
13. Downloadable game logs
I wouldn't use that, but I did some someone who wanted it for statistic, and that seems like a cool use case - unless there is some other/better way to compile stats.
14. Improved moderation (dealing with chat abuse, slowplayers, ...)
I haven't had any issues, but I haven't played that many games against other players I don't know.
15. Tutorial on how to play Dominion
I don't need this anymore, but I can certainly see the use
16. Tutorial on how to play dominion online.
Same as above
To start, a few things that aren't on the list of your specific questions:
I would like the ability to replay with the same setup of kingdom cards as last game. The use case is when playing against the AI and your strategy did not work and you want to try a different one.
I would like the ability to always exclude certain cards from a game against the AI. For example, games with chapel can get repetitive after a while, so I'd prefer to play without it.
When playing against another person, I'd like a better indication of how our rankings changed as a result of the match and why.
1. An offline client, allowing you to play campaigns against bots
Eh, an offline client isn't a big deal for me and a campaign is not a high priority either. I played the MF campaigns, and I did like that they introduced the card for each expansion at a set rate, but they were too long and Dominion doesn't seem to lend itself to a particularly good story. I wonder if some kind of 'challenges' - games against an AI, potentially with altered rules, a specific setup of cards, etc. with no attempt at story would be better.
2. A bot with a setting for different play styles
This would be more interesting in games with more players, but I generally play 2 player against the AI so...
3. A strong bot.
A strong bot would be good. I like to play against the AI sometimes because then I don't need to worry about being interrupted and I would like an AI that can handle different setups well.
4. Options for timed games
Not a huge deal, but it would be good to have
5. Options for undo settings
I would really like a better undo function. Perhaps a little undo button next to steps in the log where I could choose to go directly back to that step. Another response I happened to see described an idea where you could setup at the beginning of a game an undo policy, where you don't have to respond to every undo request, but you could set a policy about what types of actions you would allow an opponent to undo.
6. Online mini-tournaments; the option to easily create one for you & your friends.
I'm not sure I would use this feature, but it sounds like it could be fun.
7. Option to invite specific players to your table
Definitely need this! Some better searching and messaging for people would be good too.
8. More translations (to what language?)
Klingon? Just kidding. I don't need it in another language, but I'd love for people around the world to be able to play.
9. Better animations when cards are gained/bought/played/...
I don't care about animations very much.
10. Better visualization of split piles, Archive/Crypt contents, Prince targets, ...
Yes, please. And better visualization of duration cards in play would be good too.
10. Option to hide the log
This might be a good for a mobile version, but on a PC I think I'd keep the log up - particularly if the undo function is based in the log, which I think it should be.
11. Android app (or just improved compatibility?)
I might use that. I don't particularly care about app vs. improved browser compatibility
12. iPhone app (or just improved compatibility?)
I have an iPad, so I might use that as well, but I have lots of other games on it, so maybe not.
13. Downloadable game logs
I wouldn't use that, but I did some someone who wanted it for statistic, and that seems like a cool use case - unless there is some other/better way to compile stats.
14. Improved moderation (dealing with chat abuse, slowplayers, ...)
I haven't had any issues, but I haven't played that many games against other players I don't know.
15. Tutorial on how to play Dominion
I don't need this anymore, but I can certainly see the use
16. Tutorial on how to play dominion online.
Same as above