The dentist didn't find any [дырку, дупло] , so she just cleaned my teeth and took away some plaque.

cavities holes

Info: The technical word for caries in teeth is "cavities".

The relatives wondered when the old man would finally [умрет] .

croak die push off

Info: "Croak" and "push off" are of course slang.

Holmes became Moriarty's most [непримиримым] enemy.

implacable unrelenting unforgiving relentless