What would the biggest problem be? 
This is fine because "
The biggest problem would
be that" is a valid statement structure.
What would be the biggest problem? 
This is fine because "That
would be the biggest problem" is a valid statement structure.
Where is the bathroom? 
This is fine because the subject ("the bathroom") and verb "is" invert in a direct question (except in an
in situ question).
Where the bathroom is? [COLOR="#D0000"]X[/COLOR]
This is wrong because it is a direct question and "where" is not
in situ, so subject and verb should be inverted. (The
in situ form would be "The bathroom is where?".)
It is not the verb "to think" but the verb "is" that creates the flexibility:
What do you think is the problem? 
"You think that
is the problem" is a valid statement because "That
is the problem" is a valid statement.
What do you think the problem is? 
"You think
the problem is that" is a valid statement because "
The problem is that" is a valid statement.
What do you think he did? 
"You think
he did that" is valid because "
He did that" is valid.
What do you think did he? [COLOR="#D0000"]X[/COLOR]
"You think
did he" is
invalid because neither "
Did he that" nor "That
did he" is a valid statement, at least in everyday English.
Now the original questions:
Do you know where the bathroom is?
This is fine because "You know
the bathroom is there" is a valid statement structure.
Do you know where is the bathroom? OK
This is not altogether wrong, but it is unusual. "You know there
is the bathroom" is a valid but ambiguous statement structure.
"There is" could mean "hay", in which case "there" would not be a place and the question would be "Do you know whether there is the bathroom?".
But if we want to use "where" we need to be talking about a place, as in Spanish "ahí está". We do sometimes say "Here is the bathroom" (= "Aquí está el baño") or "There is the bathroom" (= "Allí está el baño"), and this is fine, but the usual word order is "The bathroom is here/there."
So "You know the bathroom is here/there" is the usual word order, and "You know here/there is the bathroom" is less common. Not wrong, but much less common.