Master Sergeant Slaughter wears six hash marks on his left sleeve to denote that he had completed 18 years of service. On his right sleeve the five overseas bars indicate two and a half years in a foreign "hostile fire area". The patch on his right shoulder indicates prior war time service in the 24th Infantry Division which fought in the Pacific in World War II and also fought in Korea, so quite possibly Sergeant Slaughter's character was a veteran of both wars. The possible goof is that in the closing scene Eustis is in dress uniform wearing the Combat Infantry Badge but has no divisional patch on his right shoulder.
As mentioned above in another goof note, Sergeant Maxwell Slaughter may be a combat veteran of two wars. Unless he rose up in ranks within 10 years (this movie is copy-write 1963,) his ribbons and awards on his chest do not reflect the two Korean awards he should be wearing. The Korean War Medal for serving within Korea. And/or Korean War Service Medal for serving anywhere during the conflict dates.Additionally, he should also be awarded The United Nations Service Medal for Korea (UNKM).
At the fair when Bobby Joe throws the stuffed tiger at Sgt. Slaughter it is moving downwards with sound effects of hitting the ground. In the next split second shot Sgt. Slaughter has it tucked neatly under his left arm.