Is alternative vote used elsewhere?
Yes, every Australian uses alternative votes to elect their MPs, and a royal commission in Britain recently recommended it to elect their politicians. A number of nations use it to elect their presidents, and dozens of cities including London, San Francisco and Oakland use it to elect their mayors. Both the federal Conservatives and Liberals use it already to select their leaders and many parties use it already to choose their candidates.  
A number of small nations including Papau New Guinea have also moved towards the alternative vote in order to encourage cooperatiom between diverse ethnic parties, and as a result of the change, election violence was dramatically reduced.
Does this benefit left or right wing parties?
Conservatives may remember the years when the Reform and Progressive Conservative voters split the vote. Liberals have the same problem sometimes with the NDP and the Greens. With alternative vote, voters can vote without having to compromise their values. This also means that parties can spend more time promoting their values than relying on fear to maintain their presence. Parties could agree to work together, but voters would still have the final say.
Does it require computers?
No. You count them by hand. It usually only takes a few minutes longer to count as the last place candidates are eliminated and elections officials will then add their votes to other candidates.
Is alternative voting complicated?
No. You can list a single candidate if you want, but if you have a second choice and your first choice does not count, your vote can go to your second choice.
Does it increase the number of politicians?
No. AV will gives voters more choices on the ballot, but voters still only pay for the same number of politicians.
Will the ballots be longer?
Perhaps. More independents may run, but voters can still look for the party names and choose the candidate who they like the most.
Does alternative voting help smaller parties like proportional representation?
Choice voting eliminates barriers such as strategic voting and allows voters to support independents or new parties without wasting their vote.  This increases competition and may help protest or issue based candidates.  However, the standard alternative voting model is not proportional and parties still have to run candidates who can appeal to over half their community.
However, alternative voting can also work in combination with a "parity vote" or "proportional additive member", in which a voter lists a candidate as well as a party. 
A more advanced version of the alternative voting, known as a single transferable vote, combines preferential ballots with multi-member ridings and can deliver proportionality.  However, it does add some complexity to the way votes are counted.
Are there better systems out there that we should wait for?
There are a lot of problems with our democracy, such of lack of fairness, distorted results, disconnect between MLAs and voters, and a lot of ideas on how to solve them. Some of them require major changes, such as various proportional systems or direct democracy, which often receive resistance from voters and politicians who benefit from the current system or prefer strong majorities.
Three referendums to bring in proportional representation at the provincial level in Canada have fallen short in the past decade, mainly because some voters felt uncertain about the proposals or had issues with some elements of them. The alternative vote will make it easier for voters to express themselves, and may elect some new voices to the legislature, while keeping the local representation that voters are familiar with.
Some of the more advanced counting systems promoted by political scientists requires computers to count the votes (such as condorcet or transferable votes) and would require major changes. Other systems allow voters to vote directly for a party and provide them with additional seats to make sure their seat count is accurate. The alternative vote can be modified in the future, if the public is ready, to incorporate some of these additions while eliminating many of the major problems in the interim.
Does anyone oppose alternative vote?
Unless someone believes that strategic voting and vote splitting are essential to our democracy, or that voters do not deserve choice, there are few critics that are strongly against it. Some politicians, who have run negative campaigns in the past, may be afraid that voters will now be tempted to vote for someone else. If they come out against choice voting, they must be really afraid of competition. Others, who strongly support proportional voting may feel that the alternative vote does not go far enough to fix enough problems and may oppose any system that is not proportional.  However, most people agree that alternative vote does fix significant problems and can be easily modified to increase proportionality in the future.