[QUOTE=QuickSilver]
I guess the more serious version of the question is; Do you have to support your arguments and do debates ever ensue over a given subject being presented by a trainee speaker (toast-grasshoper?)?
[/QUOTE]
The simple answer to both questions is “nope.” Speeches don’t have to contain arguments, but if they do then supporting them is part of having a well-developed speech. There’s no debate: speeches are presented, timed, and evaluated, but not rebutted. 
There are some advanced speech projects that allow for a Q&A period at the end of the speech, and I’ve seen that used as a time when people who don’t agree with the speech topic can question the speaker on it, but most speeches don’t include that element – none of the speeches in the basic manual do.
[QUOTE=Sunspace]
But what does “leadership” entail? Is it the kind of managerial skills that, er, managers have to learn: how to deal with erratic employees, etc? Is it how to inspire people? Is it something else?
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It’s nothing specific to working with employees – it’s not performance management kind of stuff – but you are likely to learn how to deal with erratic people in general. It’s not like you get formally trained in the leadership stuff: it’s almost all trial and error, learning by doing. I’ve learned a lot about my own strengths and weaknesses as a leader simply by taking on leadership roles within my club and my district.
Don’t get me wrong, formal training is offered for each club officer position (President, VP of Education, VP of Membership, VP of PR, Secretary, Treasurer, and Sergeant at Arms), but the training focuses on the job requirements of those positions: what you have to do and when you have to do it. The “how” is largely left up to you, and is where the growth comes in. You can certainly ask for guidance and help (which is part of learning how to be a leader, IMO), but you know your club’s members better than anyone and you know the best ways to motivate and organize them.
Another aspect of the leadership side of things is learning how to run an organized, effective meeting. Members take turns coming up with the agenda for, and running, the club meetings. As the club President, I’m responsible for running the monthly Executive Committee meetings (where all of the officers get together to discuss the club). Likewise, as the Area Governor I’m responsible for running regular Area Council meetings, where the Presidents and VPs of Education for each club in my area get together to see how their clubs are doing, exchange news, and talk about any issues they’re having.
It was well before my time (;)), but my understanding is that the role was exactly what the name implies: at formal/organized social gatherings, the toastmaster was in charge of making the toasts (which were short, public speeches). I believe they were the evening’s sort of unofficial MC.
No: you get feedback during the meeting from a person who was selected to evaluate your speech, but there are no permanent records. 
No. There are clubs where every member has finished the basic manual (10 speeches) and is working out of advanced manuals, but few of the people in those clubs intend to speak for a living. Anyone who completes the basic manual is considered a “Competent Toastmaster,” but they could have delivered 10 mediocre speeches. As I’ve mentioned before, you can’t really “fail” a speech. So being in Toastmasters, even at an advanced level, really doesn’t mean much in terms of your ability or readiness to be a professional speaker. There’s no doubt that improved public speaking and leadership skills can have a positive effect on just about any career, but the organization is definitely more about personal growth.
One of the pros and cons of Toastmasters is that all kinds of people join, for all kinds of reasons. That’s one reason why it’s important to visit a handful of different clubs before picking one to join.