In almost all cases, the opportunity and problems of drywall are the same for mobile homes as for site built houses.
However, in a mobile home, the weight is a concern. If you are replacing wood paneling with sheetrock, you are adding a lot of weight for which the home was not designed. In that situation I would suggest you consider wainscotting or some other lighter weight wall treatment and limit the sheetrock to the top half or 2/3′s of the wall.
The weight concerns are no minor matter. With mobile homes you MUST ALWAYS remember they were carefully engineered to meet the requirements but no more. They DO NOT have the reserve capacity of site built products.
Suppose you are considering getting rid of that ugly paneling in your living room and replacing it will drywall. The walls will look nicer, and provide extra sound proofing and insulation. Even one at a time the sheets are heavy so by the time you have put three or four on each wall you have added several hundred pounds.
Now think about where that weight is concentrated. It is all directly above the very end of the floor outrigers! Even if your house is on a permanent foundation, there isn’t any extra support there.
Now suppose you get a big snow storm with wet heavy snow that accumulates on the roof. Do you begin to see how easy it is to get beyond the design specifications?