The book Marge gave Homer was in the trash can in the power plant. If Homer thrown it away at the airport or where ever, then how did the book end up in another trash can?
When Homer is speaking to the Indians and thinks about what to say, he finds the book Marge has given him in a trash can. In previous shots, the trash can was not there.
Twice within the show, Carl's clothing changes in the same scene.
During the speech in which Mr. Burns says to Homer that he is a god, only the right door of the french window in the background is opened. When Mr. Burns and Smithers go away, both doors of the french window are opened.
India and the US are roughly 12 hours offset from each other; it is unlikely for Homer to talk to the kids during the daylight hours (India) as they would, likely, be asleep in bed.
Only registered Amercian citizens/residences and green card holders are entitled to benefits, pensions and government services. One purpose of out-sourcing is to cut down on taxes and costs.
Moe tells Lenny and Carl that the beer they are drinking is German. The Duff Brewery is located in Springfield.