Its reputation for the truth under attack, its stock pummeled after reporting disappointing profit numbers, the travel review site TripAdvisor Inc. has had a tough first two months as a public company. And now Google is ramping up the competition. Fifty million people a month visit Newton-based TripAdvisor to discover which hotel is “disgustingly filthy,’’ as one user called a Cape Cod motor court, or “impeccable,’’ a compliment for a historic Boston inn. Hoteliers and critics have attacked TripAdvisor and its reviews since it began posting user comments on its website 12 years ago.