While this doesn't address the leakage of the BBB itself, it does point out that there is another route that leads from the brain and into the rest of the system. The nerves themselves can provide routes of transit. Whether a dopamine molecule could follow this path or not I don't know but don't assume it is impossible.

1: Curr. Top. Microbiol. Immunol. 1995;202:63-78.

Penetration of solutes, viruses, and cells across the blood-brain barrier.

Brightman MW, Ishihara S, Chang L.

Laboratory of Neurobiology, National Institutes of Health, Bethesda, MD 20892,
USA.

The aspects presented here of how solutes, viruses and cells are able to cross
the BBB indicate that there must be an active interaction of endothelium with
viruses and immune system cells before they can penetrate the brain and spinal
cord. The axoplasmic pathway taken by lectin-solute conjugates is similar but not
identical to that followed by viral particles during their retrograde or
anterograde transit through the axoplasm. Both the conjugates and virus are
transferred to other neurons transsynaptically but the receptor mediated transfer
utilized by viruses is far more specific. Cranial nerves are involved in both the
entry and egress of antigens into and out of the brain. Antigen, generated within
the CNS, may be able to escape from the brain to lymphoid tissue by passing into
the fluid around a cranial nerve, thence via the lymph into lymph nodes to
initiate an immune response involving the CNS.

Publication Types:
Review

PMID: 7587371 [Pubmed - indexed for MEDLINE]