Short answer:
The Florida vote count became a mess because Florida election law was not properly or completely followed.  A close reading of Florida law suggests that all the votes the Democrats wanted counted were probably supposed to be counted during the initial canvassing of votes or during the automatic recount (click here for more details).  A close reading of the Florida law also suggests that all the vote counting was supposed to be wrapped up by November 14 (except for absentee ballots).  However, since so many of the machine rejected ballots went uncounted, Gore used the protest provision of Florida election law (Section 102.166) to try and get them counted.  This provision seems to provide an overtime for vote counting  (i.e., counting beyond the 102.112 deadline) in counties where the vote count may be inaccurate and such inaccuracies may be affecting the election outcome.  However, it probably would not have been necessary to try and get these votes counted as part of a protest pursuant to 102.166 if they had been properly canvassed pursuant to Section 101.5614, of Florida's election code,  1S-2.0031 of Florida's election rules, and DE 90-46 issued by Florida's Election Division during the first count or automatic recount .
 

Long answer:
A close read of the much maligned Florida election law reveals that the debate regarding return deadlines and machine unreadable ballots could have been avoided had the law simply been followed from the outset.

The uncounted vote issue deals with the more than 130,000 ballots yet uncounted in Florida despite being processed through the counting machines.  The Gore campaign is asking that thousands of these “lost votes” from Dade County be inspected for votes.  However, this effort to count Dade’s yet uncounted votes begs a question that has been circling for weeks now in this election: why not count all the uncounted votes across the state, instead of just the ones in the 4 South Florida Counties?

A closely related and highly litigated topic is the deadline for vote counting. The Secretary of State and the Bush campaign contend that November 14 was the statutory deadline for all ballot counting except absentee ballots.  The Gore campaign and the Florida Supreme Court contend that the statute’s deadline is contradicted by another provision that allows counties to begin a lengthy manual recount process on the same day that its returns are supposedly due.

A brief overview of what was legally supposed to happen in Florida suggests that both the uncounted ballots and the counting deadline are only issues now because of poor compliance by the County Canvassing Boards and the Secretary of State.
All the state’s  tens of thousands of uncounted ballots were supposed to be inspected for voter intent by local canvassing boards as part of the canvassing process delineated in 101.5614 (5): “If any paper ballot is damaged or defective so that it cannot be counted properly by the automatic tabulating equipment, the ballot shall be counted manually at the counting center by the canvassing board…No vote shall be declared invalid or void if there is a clear indication of the intent of the voter as determined by the canvassing board.”  A manual inspection of just the thousands of machine-rejected ballots across the state
could easily have been completed prior to the November 14 deadline.

Most counties, especially large ones, probably do not comply with this mandate on election night because the machine count alone typically generates a lead large enough to render unnecessary a manual inspection of the typically small percentage of machine unreadable ballots.  But Bush’s lead following the first machine count stood at roughly 1,800 votes out of about 6,000,000.

Because the election was so close, Section 102.141(4) required that every county go back and recanvass their ballots, a process that would presumably be a repeat of the previously quoted 101.5614 requirements for canvassing returns.  The
stakes were high enough and the vote close enough to warrant full compliance. However, only 10 counties (7 of which were won by Bush) actually conducted a statutorily sufficient recanvass that included another machine count and manual
counts of machine unreadable ballots.  The remaining 57 counties did something less.

If every county had conducted their canvass pursuant to Florida statute, then all of Florida’s now uncounted ballots would have been reviewed.  Florida law assumes as much under Section 101.5614(8): “the return printed by the automatic tabulating equipment, to which has been added the return of write-in, absentee, and manually counted votes, shall constitute the official return of the election.”  Even the largest counties could have manually inspected just their uncounted ballots in a matter of days, as opposed to the weeks it takes for a large county to conduct a full manual recount.  Given these statutory requirements, the Florida Statute’s November 14 deadline for county returns is not so unreasonable or contradictory.  Had all the votes been properly canvassed, Gore’s efforts to get these uncounted votes counted in 4 South Florida counties by requesting full manual recounts pursuant to 102.166 would have been unnecessary.  In other words, outside of obvious machine error or voter fraud, there would have been no reason to continue counting past the November 14 deadline as the protest and full manual recount provisions allow.

Why were so many counties allowed to conduct statutorily inadequate canvasses? First of all, the Secretary of State imposed a one-day deadline for the recount, which only gave counties with about 100,000 ballots or less time to manually inspect machine unreadable ballots (Seminole’s recanvass of 130,000+ ballots took 30 hours).  However, the true deadline for these returns was November 14. Clearly, every county canvassing board across the state had the necessary time to conduct a proper canvass; for whatever reason, they chose not to.

The next break down was at the Secretary of State’s office.  Her first duty under Section 97.012 (1) is to “maintain uniformity in the application, operation, and interpretation of the election laws.”  Clearly, a few counties complied with the full extent of the law, while the overwhelming majority did not.  To maintain uniformity in statutory compliance and to insure the full application of Florida’s canvassing provisions, she should have required every county to do what 10 already had -- a complete canvass pursuant to 101.5614. Every county could have followed these canvassing guidelines to the letter and still filed their returns with the state by the November 14 deadline she so dutifully imposed.

Florida Law makes sense, it simply was not properly followed and enforced.