Eu tenho trabalhado com uma instalação MAMP por várias semanas agora, e quando eu comecei hoje não seria iniciado. Nenhum processo mysql estava rodando, então eu verifiquei o log de erros que mostra o seguinte quando eu inicio o servidor:

130826 14:19:55 mysqld_safe Starting mysqld daemon with databases from /Applications/MAMP/db/mysql
130826 14:19:55 [Warning] You have forced lower_case_table_names to 0 through a command-line option, even though your file system '/Applications/MAMP/db/mysql/' is case insensitive.  This means that you can corrupt a MyISAM table by accessing it with different cases. You should consider changing lower_case_table_names to 1 or 2
130826 14:19:55 [Warning] One can only use the --user switch if running as root

130826 14:19:55 [Note] Plugin 'FEDERATED' is disabled.
130826 14:19:55 InnoDB: The InnoDB memory heap is disabled
130826 14:19:55 InnoDB: Mutexes and rw_locks use GCC atomic builtins
130826 14:19:55 InnoDB: Compressed tables use zlib 1.2.3
130826 14:19:55 InnoDB: Initializing buffer pool, size = 128.0M
130826 14:19:55 InnoDB: Completed initialization of buffer pool
130826 14:19:55 InnoDB: highest supported file format is Barracuda.
130826 14:19:55  InnoDB: Waiting for the background threads to start
130826 14:19:56 InnoDB: 1.1.8 started; log sequence number 4057202289
/Applications/MAMP/Library/bin/mysqld: File './mysql-bin.000025' not found (Errcode: 2)
130826 14:19:56 [ERROR] Failed to open log (file './mysql-bin.000025', errno 2)
130826 14:19:56 [ERROR] Could not open log file
130826 14:19:56 [ERROR] Can't init tc log
130826 14:19:56 [ERROR] Aborting

130826 14:19:56  InnoDB: Starting shutdown...
130826 14:19:57  InnoDB: Shutdown completed; log sequence number 4057202289
130826 14:19:57 [Note] /Applications/MAMP/Library/bin/mysqld: Shutdown complete

130826 14:19:57 mysqld_safe mysqld from pid file /Applications/MAMP/tmp/mysql/mysql.pid ended

Portanto, é claro que determinado arquivo de log não pode ser encontrado, mas não sei por que isso aconteceu ou como corrigi-lo.