The September 11 terrorists had purchased first-class, one-way tickets, so passengers with one-way tickets were more likely to be flagged for additional screening after that date. Your boarding pass could be flagged with the letters SSSS, triggering additional screening. Or the airline gate agent might not accept your bags until they were hand-inspected.
That was a long time ago.
Although there are still people who think that one-way tickets increase the chance of being selected for an additional security screening or baggage inspection, that seems unlikely to me. Presumably the TSA watches for suspicious activity, but I can't see how one-way tickets constitute any sort of additional risk. In fact, someone with evil intent would be more likely to buy a roundtrip, given even the slight possibility that a one-ticket would trigger more scrutiny from the TSA.
These days, many leisure travelers buy two one-way tickets, often using two different airlines, instead of buying a roundtrip itinerary on a single airline. Decent leisure fares used to require the purchase of a roundtrip with a Saturday night stay. But that's seldom the case these days for domestic flights.