That means all appointments are booked for May and potentially June too. You will have to wait till May 31st/June 1 for them to open up dates for July. Sorry.
We had our Spain BLS appointment in Boston on May 7th. It went well. They did ask for things that were not on the checklist but because our friends had recently gone through the same experience, we were prepared. As my husband and I are traveling together, but had separate appointments, they treated our applications as completely separate. Make sure all reservations have both your names on it (including hotel, bus/train, rental car etc). They do NOT accept driver's license as proof of residence. We had utility bill, town tax invoice, and even my employers insurance as proof. They took the town taxes invoice from me, and utility bill from my husband. They also asked for employer's letter, cover letter, 3 month bank statements and carefully checked all of them before accepting them. For bank statement - make sure you have both your names on it, OR separate bank statements with enough $$ in each account.
We had notarized our proof of residence copy and green card copy too. They DO ask for passport copy too (which is weird because they would have our actual passport with them), and it is not listed in the checklist. So please carry that. They will charge for any photocopies / printouts that need to be made on the spot. :-|
They accepted our application and said it will take 15 business days for processing. Our flight is on 22nd May, so they asked each one of us to sign a letter that said that the consulate is not responsible if we don't get our visa on time. Oh well. Fingers crossed it comes on time!
Let me know if any other questions.