Doug Takes a Hike / Doug Rocks - S1-E4
Continuity mistake: When Roger is dancing in Skeeter's yard, he changes color.
Other mistake: A time card reads 6,000,002 BC, when it should've read "60,000,002 BC". (00:07:12)
Bug Off/The Crawl Space - S9-E5
Continuity mistake: In Moving Away, Tommy tells the other Rugrats how they first met when Angelica lied about the nasty things they did. However in the Crawl Space, there is a flashback of Tommy, Chuckie, Phil and Lil playing in the playpen when they were younger. Chuckie is scared of the Jack-in-a-box in that flashback, so the Rugrats could not have met for the first time back then.
The Retainer - S1-E2
Other mistake: The gas chamber is destroyed when the dogs pull a chain that's attached to its front support but it somehow collapses from behind. (00:19:07)