I enjoyed the I.M. effects very much and I never spotted a wire; however, quite often, things like telephones, pens and cigarettes behaved strangely when lifted by the invisible man: they tended to somehow oscillate, a movement not to be expected from an object supposedly held by a hand (invisible or otherwise).
Nevertheless, it was good and fun. ALL 26 EPISODES ARE AVAILABLE FOR WATCHING OR DOWNLOADING at Internet Archives dot org (Classic TV Section) or at Uncle Earl's Classic TV web site. Don't miss them.
I also agree with the previous commentator that ITC, very markedly at that time, usually offered products of a superior quality. I'm an admirer of Ralph Smart (the producer of this series), who would be later responsible for the excellent and unsurpassed Danger Man (Secret Agent Man) starring Patrick McGoohan.