What are some signs of infection after periodontal disease surgery?

Several things: Swelling, pain, pus, and redness are the most obvious signs. If you have those signs, contact your dentist who did the surgery.

It's rare to get it: It is very unusual to have infection after the periodontal surgery, specially if u were placed on some antibiotics afterwards. Nonetheless, if it happens it will be with severe redness, very warm/ hot cheeks, severe pain, ; unusual swelling, very bad breath, possible pus/discharge from gum lines and oozing thru, and possibly even fever. Make sure you contact your periodontist or dentist(?).