This is a complication because the only real answer to Juliet's problem is to marry Paris. She is already married to Romeo but she knows her parents extremely dislike him so she cannot use that to save her.
"Juliet is dead"
She is dead!
This is a complication because Juliet wants to die if she has to marry Paris and can't be with Romeo. Friar Lawrence comes up with a plan to fake her death but doesn't think the whole thing through. Romeo doesn't know this is fake and could take his life before she wakes up.
She must've been killed
This is a complication because Juliet has taken the vile and soon they will discover her. Since Romeo is a Montague and he killed Tybalt they could suspect that he did it.
Prepare the funeral
This is a complication because everyone thinks Juliet is dead.
This is a complication because the Capulet's believe that someone killed Juliet and they will have to find someone to blame.
This is a complication because instead of having a wedding now they are going to bury Juliet but little do they know she is just sleeping. Word will spread and everyone including Romeo will think she's dead.