I know there are several areas than need addressed when rescaling a model but I can't give any specifics since it isn't an area I'm familiar with from experience or that I've read much on so I have to rely on just "Southern Engineering" principles... LOL
There are considerations in strutural strength for the materials being used. The increase in mass results in gforces that often exceed what a smaller model can handle easily requiring stronger materials in the areas affected in the larger model.
3DHS has recently released a new 48" Edge where they changed the horizontal/vertical stabs etc over too airfoiled versions from flat. They also went from CF LG on the 48" to the steel rod type that the 41" has had great success with, but are having minor reports of strength issues when using them on the larger version. They also had an older 55" version and upscaled to 58", the redesign has taken over a year to get from the drawing board, through prototyping to distribution.
Hobbyking recently, last year or the first of this year, released a SBach made by some company that I've already forgotten the name of.... It was almost a complete bust with the majority of the complaints saying the model comes out very tail heavy... Turns out they had simply scaled down a larger model that did work well but didn't prototype it as a smaller model before starting to sell them... The only guys that were successful flying them did it by rebuilding the tail surfaces lighter and then the model still had a higher wing loading than they cared much for.
Another area that must be addressed is the power plant. I'm not sure if the increase in power must be logarithmic or exponential but I do know it isn't a linear increase. The way I've always heard this refered to is that "the air doesn't scale"... in otherwords the drag increases for the size of the model and that the lift produced by a wing type differs as well but not linearly.
I know my father has rescaled many planes in the past and usually doesn't have much trouble but he had been doing it since before I was born also, so I suspect he just naturally makes adjustments during the building and probably doesn't think about it much these days. The following are areas that I'd think ( but not know for certain ) that should be addressed...
Beef up the landing gear and the LG block area. Not only building just the immediate LG block stronger but also spread out the forces it will need to take both forward and rearward from the block. I used two carbon fiber tubes that extend from the F1 former ( the former the motor box sticks out from ) to the former just behind the LG block area along with some CF sheeting in the LG block itself on my 51" Slick to do just this... works great. On the last bad landing I made ( was having elevator issues in flight ), I came in very hot on landing and my gear sheared off cleanly without damage to the fuse. I suspect the same landing on an unmodified LG block area would have ripped that whole area out instead.
A slight increase in the strength/size of the wing spars to handle the additional mass of the plane better. Do a similar increase in strength on the tail surfaces either by going with airfoiled pieces or by using harder wood like bass wood in some of the key areas here near where they attach to the fuse.