The first problem with integration is that the larger the diaspora community is in an area, the more difficult it becomes to integrate with the host culture. There's no need to learn the host language if you live in an area where every one speaks yours. There's no need to mix with the host citizens if your community is large enough to provide jobs for you in a climate where your home culture holds sway.
An example here would be the difference between a Brit living in Benidorm as opposed to, say, Seville.
It is also the reason why migrants prior to the late 70s, regardless of background, integrated better than modern migrants. Because they simply had to. Otherwise, they would starve.
The second problem is that the more isolated from wider host society the community is, the more its diaspora expression of its "home culture" ossifies because it doesn't evolve with the wider host culture and may even set itself against it, but is also disconnected from evolutions occurring in the "home culture" itself.
The "home" culture in a diaspora context tends to be transmitted by family and other members of the community, rather than the wider society as a whole as would occur in the home country itself, so the culture of a diaspora is usually the culture of the home country that existed some ten, twenty, thirty or more years ago.
An example of this would be minority communities that live in a way and hold values that seems very old-fashioned and out-of-date to modern citizens of their home or origin nation. For example, the Lebanese community in Australia as opposed to modern Lebanese citizens in Lebanon itself. Pakistani communities in Britain as opposed to urban Pakistanis in Pakistan. Kashmir is also quite a noticeable example where modern Kashmiris living in Kashmir seem to have very different ideas and values to second or third generation British Kashmiris.
An example of this can be seen in something like the film "My Big fat Greek Wedding", which, although is a satire of sorts, quite accurately depicts that diaspora behaviour whereby third generation American Greeks somehow need to be more Greek than the Greeks themselves, and the Greek culture they perform is a culture that hasn't really existed in Greece for decades, if it ever did.
All this gets in the way of integration. I've seen it myself coming from a multicultural family, as does DH. Although DH and I are utterly assimilated (I think 
), as is my DM and MIL, there are still flash points where there is a desire for both my DM and MIL to define themselves against "the English".
A lot of it is about notions of identity and selfhood that cannot be easily picked apart. Personally, I think the mass immigration of the last twenty years has been a total disaster, purely because the numbers of migrants involved has made the circumstances required for integration pretty impossible.