Sometimes in a meeting where a problem is being discussed I'll say something like "Perhaps we should consider frobnigating the widgetron instead of hexterpating the frampilator. I'm not saying that's the right solution, just throwing it out there for consideration." Does it reflect badly on me to propose alternatives without necessarily recommending them? Is it likely to be perceived as wasting my co-workers' time, being too wishy-washy, or lacking leadership qualities?
No, it does not reflect badly. Your idea may be the thing that spurs some other idea that is percolating in someone else's head. This is how collaboration works. Additionally, if you want to be a leader, you want people on your team to not be afraid to toss ideas into the ring. You demonstrate this by doing it yourself. This is a strength.
It depends on the goals of the meeting.
If it's a brainstorming meeting, then it's usually most desirable to generate many alternatives quickly before trying to judge their worth. In this case you wouldn't be wasting time.
If you are being asked to come up with alternatives without regard to your recommendations, then your reply wouldn't reflect badly on you.
If you think your suggestions might be viable, but you need the group's input to reach your recommendation, then your approach is reasonable.
But if this is an urgent "what should we do about this problem" sort of meeting, it seems to be implied that you are being asked for your recommendations. In that case, generating a bunch of alternatives that you wouldn't recommend might be considered a waste of time.
Additionally, consider your role in the meeting. If you are the team leader, then you might be tossing out a bunch of ideas soliciting feedback from your team.
But if you are the sole technical expert for a technical question, then it may be implied that your specific recommendation is being solicited, not get a list of possibilities.
And it also depends on the overall viability of your solution. Tossing out solutions like "first we boil the ocean (not that I'm recommending that, I'm just throwing it out there)" isn't likely to be received well.
Context is everything in meetings.
First, it depends. The purpose of the meeting really dictates the appropriateness of this sort of thing. In brainstorming meetings this can be invaluable as often bad ideas only need the tiniest adjustment to be good ones. In meetings where you've already established and developed everything and are doing fine tuning this may not be as appropriate.
When to suggest ideas
Typically project meetings break down into three types, Brainstorming, Planning, Review
A brainstorming meeting is the perfect place for this. You bounce ideas back and forth until something sticks and you agree it's what you want to go with. (this can span multiple meetings)
Planning alternative suggestions that are reasonable isn't a terrible idea, but you also don't want to get over the top with them either. Small adjustments in planning are fine, major adjustments cost time, your suggestion needs to merit that use of time at this point.
Review meetings happen periodically to check the progress of a project as it goes along. While your plans are never in stone until they're done, at this point the plans are pretty solid and only minor adjustments are worth discussing.
Non-technical managers tend to want solutions delivered to them with confidence. There is a communication gap in these cases. An engineer is not going to say "I'm sure I can do it." if he really thinks he's 90% certain. Most managers would show confidence at 75% or less. They don't live in a world of absolutes.
Is your job to come up with suggestions or make decisions? There is a big difference. If you are in a room with other qualified people, they shouldn't need you to "sell" them on your idea or for you to take a leadership role. Among technical peers, a good idea should stand on its own without any strong persuasion.
Do you find yourself giving ideas to people who just don't get it?
Throwing out solutions without evaluating their appropriateness and without weighing their pluses and minuses is a useless act, because no solution is worth anything if the rationale for offering this particular solution isn't there and there is no analysis as to what circumstances the solution is best for and to what circumstances the solution would backfire, or what resources including time commitment the solution would require. It is also acting like a jerk, because the hard work of evaluating and validating these solutions is left to others.
Throwing out solutions without analysis or commentary is like throwing paint on the wall and seeing what sticks. It's also like talking without taking any personal responsibility for any of the words.
If a subordinate or a colleague did that to me, it wouldn't go well with me.
Having said that, a brainstorming session is specifically designed to elicit ideas and especially ideas that are out of the box. In the specific context of a brainstorming session, you are not required to fully analyze those solutions that are thrown out.