These are the changes I have seen.
Lua 5.1 API incompatibility with Lua 5.2 beta rc-2
==Removed==
LUA_GLOBALSINDEX
LUA_ENVIRONINDEX
lua_getfenv
lua_setfenv
luaL_typerror
luaL_putchar
lua_yield
==Compat removed ==
luaI_openlib
luaL_getn
luaL_setn
lua_ref
lua_unref
lua_getref
lua_open
lua_getregistry
lua_getgccount
lua_Chunkreader
lua_Chunkwriter
luaL_reg
==Requires LUA_COMPAT_ALL==
lua_cpcall
lua_strlen
lua_objlen
lua_equal
lua_lessthan
==Signature changed==
lua_pushlstring
lua_pushstring
==Structure changed==
luaL_Buffer
lua_Debug