die Gründlichkeit
thoroughness. The Duden defines it as conscientiousness and care.
akribisch
meticulous, extremely thorough, as in akribisches Quellenstudium, meticulous study of sources
auf Herz und Nieren prüfen
to test someone or something thoroughly, literally on heart and kidneys. The Duden traces it to Psalm 7.
unter die Lupe nehmen
to examine closely, literally to put under the magnifying glass
German also has words that mock checking that has lost its purpose.
der Erbsenzähler
the pea counter, a petty and stingy person
der Korinthenkacker
a crude word for a petty and pedantic person, literally a person who defecates currants
die Haarspalterei
hair-splitting