More than anything else I see ecumenism as a great hope for religion--and quite possibly for those who don't like religion much as well.
What Christians would like ecumenism to be is a gathering of the whole church--a church mostly broken up by culture, geographical boundaries, and petty human actions.
In practice ecumenism works out to several different "ecumenical" groups. Left leaning (liberal)denominations tend to be in ecumenical groups with other left leaning denominations. Conservative denominations tend to be in ecumenical groups with more conservative denominations.
If anywhere, true ecumenical action occurs in small, local church councils (I've worked for two of them) where concern for one's city prevents the usual political or theological squabling.
Personally, I don't see this as problem particular to religious organizations. I practiced Tae Kwon Do for several years and was amused to find groups constantly splitting off from the main group. Close your eyes for just a second and bam--it's a schism.
What's cool about ecumenism is that even if Christians aren't necessarily accepting all other denominations, they're making more of an effort to so than they used to. And some are accepting of other religions (or lack thereof) as well.