In her first appearance in the Pilot episode, Hayley is shown to wear tan opened toed sandals.
In "Deacon Stan, Jesus Man" has Hayley wear sandals while wearing a strange looking outfit at Church and when she's wearing her normal clothing.
"All About Steve"
In "Stan of Arabia: Part 1", Hayley is seen with sandals while wearing a robe as she and the other Smiths are now living in Arabia. Oddly, in most scenes she appears to be wearing regular shoes.
In "Star Trek" Hayley in sandal feet while booing at Steven on TV.
In S2E10 "Bush Comes to Dinner" Hayley's right sandal is missing, revealing her right foot.
In S2E11 "American Dream Factory" Hayley's right sandal is missing, revealing her right foot again.
In S3E1 "The Vacation Goo" a few barefoot images
S3E4 "Big Trouble in Little Langley"
In S4E2 "The One That Got Away" she is barefoot while playing a hypnosis game.
In S4E6 "Pulling Double Booty" Hayley is barefoot while next to Bill.
iN S3E12 "Roy Rogers McFreely" a few images of Hayley's sandal feet.
In S4E13 "Jack's Back" a few images of Hayley's sandal feet while having a dress-outs contest.
In S5E03 "Home Adrone" a few shots of Hayley's Sandal feet when she and the others spent 16 hours on a plane to Boston.
In S5E17 "An Incident at Owl Creek" she is barefoot while wearing her Great-Grandmother's swimsuit.
In S6E2 "Son of Stan" a few images of Hayley in her sandal feet and bare feet in a red bikini while Roger, who wanted the $50,000.
In S6E16 "Jenny Fromdabloc" a young Hayley wearing purple sandals and is barefoot while brushing her hair.
In S7E6 "The Scarlett Getter" a couple of Hayley barefeet and a close up of her sandal feet.
In S7E11 "Old Stan in the Mountain" an image of Hayley sandal feet as she is looking at a latin book.
In S8E1 "Love, American Dad Style" she is barefoot while her limbs are tied on the bed.
In S8E2 "Killer Vacation" she is seen wearing purple sandals
In S8E6 "Adventures in Hayleysitting" she is barefoot while on the couch and a close up of her sandal feet when she is pressing the pedal.
In S8e19 "Da Flippity Flop" a close up of Hayley Sandal feet when she and Francine surround Klaus (who was in Stan's body)
In S9e2 "Poltergasm" she is barefoot while kissing her new boy toy.
In S9e7 "Faking Bad" a shot of Hayley's sandal feet while she's in jail for making fake I.D.'s
In S9e9 "Vision: Impossible" a few close up of Hayley's sandal feet, including one with also shows her heels.
In S9e16 "She Swill Surivie" Hayley is barefoot while wearing a purple robe.
S9e19 "News Glance With Genevieve Vavance" has a few shots of Hayley's sandal feet as she wears a news suit. Also the sandals are dark brown instead of Tan.
We need the episode sources for this.