The disadvantages typically relate to the cost of the infrastructure -- arenas and stadiums cost hundreds of millions of dollars, and in some cases even roadways and offramps to the facilities are built at public expense. The worst-case scenario is when a city builds an arena to attract a team, but fails to do so. Kansas City is an example, having built for an NHL/NBA team that has never arrived. Hamilton, Ontario built an NHL arena in the 1980s but has only attracted minor league hockey. There is the potential, then, that major investments can result in little more than a white elephant. The benefits differ between leagues as well. The NFL scores high for exposure but has fewer games, whereas MLB has a large number of games. The NHL is only a driver of substantial revenue for hockey markets, so it works better in Columbus than it has in the Phoenix area, for example. NBA and NHL arenas are cheaper to build than football or baseball stadiums, and they can be dual purpose, reducing the costs even further.

It is worth considering that there are different means to attract teams. Building stadiums is the most costly, and the economic benefits may not be apparent depending on the cost of financing the stadium. Tax incentives are less likely an enticement,...

It is difficult to put a price tag on exposure -- how much investment does a cold, northern city like Green Bay genuinely attract as a result of the Packers? -- but for a city seeking to raise its profile, at least some money spent will pay off. More critically, the benefits only arise when a franchise arrives. Spending in pursuit of a team is a poor choice for cities -- spending to service a franchise that has been granted to the city makes more sense.
Works Cited:

deMause, N. (2010). Memphis chamber: Grizzlies arena is grrrr-eat! Field of Schemes. Retrieved February 14, 2011 from http://www.fieldofschemes.com/news/archives/nba/memphis_grizzlies/

Morgan, M. (2010). Net gain for Memphis: Study finds Grizzlies, FedEx Forum more than pulling their weight at making sizeable financial impact on area. Commercial Appeal. Retrieved February 14, 2011 from http://www.commercialappeal.com/news/2010/oct/04/net-gain-for-memphis/

Thompson, L. (2009). Glenn School study finds big economic boost from Columbus Blue Jackets and arena district. John Glenn School of Public Affairs, Ohio State University. Retrieved February 14, 2011 from http://glennschool.osu.edu/news/bluejackets.html