Also, I can suggest using user created shared parameters instead of the default REVIT ones like "Mark" and "Type Mark". By default, REVIT will never automatically assign the same value of "Mark" to new elements ... so you'll never get that warning again even if REVIT autoassigns new (and ignored) values for "Mark".
That statement is not true if working in a workshared environment. If two people are placing the same category of element in a model then Revit will continual to assign the next number in the Mark sequence to each user's local copy. Upon Saving to Central the Mark error will be generated.
You can turn off calculations if you are only doing modelling and they are not required. However if they are required I would suggest that you resolve the systems issue properly.
No loss defined - Check the system is built properly, the correct sized fittings/accessories have been used so they can access the ASHRAE loss coefficient tables and also that duct shoes have a loss coefficient or specfic loss applied.
A new issue that arises in 2012 is linking no global connectors. Previously if you linked non-global connectors, Revit didn't do much. Now however, you can get the flow mismatch error if you try and link a supply connector to a return connector (for example) - so go edit you families to remove linked non-global conenctors.
Not well connected error is a pain to resolve as it is not always easy to find to the problem. Sometimes a simple delete the system (not all the ducts,, fittings, etc.) and re-create the system works. Sometimes you have to check that all elements are perpendicular/parallel/set at the exact correct angle as designed. By this I mean the connection is 30 degrees and not 29.999968 degrees.
Fix that overlapping lines error - not sure how you forced Revit to have elements that accept this error as normally you can't do a filled region or create inplace geometry with this error.
The Mark value issue as mentioned in an earlier post is not a massive issue that will kill performace - so ADSK have advised me in the past.