Multiple start and stop codons in mRNA and pre-mRNA
Whether or not there are multiple start and stop codons depends on what you mean by "start codon" and "stop codon". 

The start codon has the sequence "AUG", and the stop codon has the sequence "UAG", "UAA", or "UGA". Both the pre-mRNA and the mature-mRNA can, and usually do, contain multiple instances of all of these sequences. However, only one "AUG" instance serves as the translational start site, and only one instance of the stop codon sequence serves as the translational stop site.

The translational start site is usually the first (5' most) AUG. However, for reasons that are still not entirely understood, in about 5% of genes the first AUG is skipped, and translation starts at one of the other AUG sequences.

The translational stop site is always the first stop codon to occur in-frame with the translational start site in the mature mRNA.

The stop codon is usually not (I'm tempted to say never) the final sequence before the poly-A-tail. The coding sequence (the RNA region that codes for the protein) occurs in the middle. There is a 5' untranslated region (UTR) before the protein coding region, and a 3' UTR after the protein coding region. The UTR sequences vary among genes and can have different functions depending on the sequence.