I run with mixed groups all the time

There are pros and cons though:
Pro's:
- You get a good mix of different classes so can basically select what you feel is the 'best' team
- there's no real deal-breakers stopping you from having a mixed group

Con's:
- They won't all recall to the same home town - but this is really only a problem at the start as honestly, from about 20 onwards I rarely if ever go back to 'home'. This con can be minimised now as, since a few patches ago, there are a lot more travel bells so really - give it 5 mins and your all back together.
- 'Some' zones do have faction quests - from memory Ferrot has two faction camps requiring you to send the appropriate people to each camp to get the same quest (just differently named) - but really, no other zone really sticks out in my memory which has the 2 different quest lines
- really will only be a problem if your say < level 20 as you may be doing your home town quest series - but that can be totally avoided as you can get more ebenfit from going to TD and doing that line of quests

A mixed group can walk into any town - after a certain level - is it mid 40s? totally gone form my brain atm but if your team is 50+ there is no worries - all the guards will be grey. When the game was released you couldn't walk into any opposite faction towns but now most of the guards have been either removed or are low level.