he saw "communists" where none existed
Can you give examples?
For example, his famous "list of 57 communists working in the state department" that brandished didn't actually exist. He said he had "penetrated the iron curtain of State Department secrecy" while hiding that most of the names came from the Robert Lee list that had contained mostly named that had been cleared. McCarthy constantly exaggerated the loyalties of the people on the list, converting "has some sympathies for communist causes" to "a communist." He was good at using rhetoric, but rarely produced any evidence towards a person.
I can say of the nine people charged by McCarthy at the Tydings committee, the evidence against four of them was very flimsy (and they were later cleared by loyalty boards), and the evidence against these five was even weaker:
Dorothy Kenyon, a feminist who did some work for the UN (good enough for McCarthy to charge her as a communist), who lost her civil service job as a result of McCarthy's allegations.
Esther Brunauer, who left Germany when the Nazis came to power, and converted previously-pacifist to more specifically anti-isolation and anti-Nazi stances at the start of WW2. After the war, she came under attack from isolationists, but Senator Joe Ball stated she was "perhaps the most violently anti-Communist person I know."
Gustavo Duran, who joined an anti-Communist faction during the Spanish Civil War. McCarthy claimed that in a picture from that time, he was wearing a uniform of the SIM - The Russian military intelligence. The uniform was actually the Spanish military uniform. No communist ties were ever proven.
Owen Lattimore, who made some pro-Soviet Union statements. Specifically, during World War II, he was in favor of the USSR's foreign policy of international cooperation against against the Axis Powers of Japan and Germany (before the US's entering the war), and due to that he published an article by a pro-Soviet writer who wrote favorably on Stalin's purge trials to strengthen the Soviet Union against the upcoming war on the Axis Powers. It was absolutely the biggest blunder of his career, and his own editorials arguing against allowing a communist takeover of China didn't erase that stain. Later reporting on how good things looked at a sanitized Russian labor camp did not help his position either. His writings were "superficial and uncritical", but McCarthy trumped up the charges and turned it into "Owen Lattimore is a top Russian spy." No proof was able to be produced, later declassification of intercepted Russian cables mentioned Lattimore, and a retired FBI agent 30 years later said they never had anything substantial against him.
Harlow Shapley was one of the nine people charged in the Tydings hearings, but I can't find much information here. Despite the report's statements, Shapley was not in the State Department, working as an astronomer with the Harvard College Observatory. He was known for his public contempt for HUAC, but these days contempt for that group is pretty reasonable.