I have discussed this issue many times and I don't have the time at the moment to go into it.
Indeed there are some who believe that Rebbe was Moshiach, but they are a very small minority in the Chabad organization. I have discussed this topic with my Chabad Rabbis and it is clear to me that while the Rebbe is definitely a model for all Chabad emissaries (what they call their Rabbis who set up Chabad houses around the country). I know several Chabad Rabbis and have discussed this with just about all of them, and they do not believe or teach that Rebbe was Moshiach.
I have a lot of respect for Rebbe of Lubavitch and believe he, like some of the other greats of our generation, had a spark of Moshiach.
Rebbe and Chabad have always supported the state of Israel and they are doing great work getting Jews to keep their Jewish identity, and ensuring they have the opportunity to do the mitzvot (by providing candles for Shabbat, and Matzah for Passover)....
If you would like, do a search on Messianic Chabad on this site. I am sure you will find some of my discussions of the topic.
It is sad that some people have distorted the teachings of Chabad as an organization. I do not believe that the Messhichists in Chabar represent the majority opinion on the topic. And I have also known people who were brought up in Chabad homes who say that it is a small minority who believe that the Rebbe was moshiach.