My child's mid-year skip last year from 3rd to 4th was mostly positive, but not without some stress. The child had been begging for a skip for years and at the start of 3rd was sent to 4th "part-time." Schedules became complicated and he started to feel as if he had no home base and to resent the time he continued to spend in 3rd. He would do all of his "4th grade" work (which was actually 5th, 6th, 7th + as it's mixed age/grade with a lot of subject acceleration) and none of his 3rd grade work. It just became clear to everyone after about 8 weeks that there was really no point in continuing with 3rd. Bonus: I think the 3rd grade teacher was glad to be rid of me. I was always pestering her for something. Honestly, she couldn't sign that paper fast enough once the principal presented it.
Because it was 3rd to 4th, there were quite a few changes organizationally and executive function was an issue. I had to provide a ton of scaffolding for at least 3 months because after so many negative experiences I was determined to do anything I could do to help this be positive. He had never had to keep his own binder, for example, or write down his own homework. I stayed on top of it and taught him how to do the things that the other children had already had 2 months to learn.
As for reactions from the kids -- my child felt vindicated -- he had felt powerless and voiceless for far too long and his drive to be more challenged had finally led to someone (his new teacher) respecting that. His confidence has increased tremendously. He is still plagued by self-doubt when he becomes overwhelmed, but even that is starting to diminish. Being moved up was far more important to him than anything social, though he did leave behind a best friend who he adored and this was not an easy thing for him to do. We made a huge effort to have as many playdates as possible, but new friends have since been made and things have settled into a routine. We were very lucky as there were already 4 other children in his receiving class who were grade-skipped, so this is was not un-heard of. Most kids think my DS is older anyway, because he's very tall. They did "graduate" him in his 3rd grade class -- but it was very hasty as the skip happened one week after we signed the papers.
As for the parents, those in my support group were supportive, those who were not weren't told by me. Because the holidays were upon us (this happened in November) many people did not even find out until much, much later. I suspect there may be a few who still do not know. I did have one parent approach me and ask if he had been held back the previous year -- "was that why they moved him?" I just said no.
There probably could have been more planning -- to some extent we all winged it. But, in a way, that made the entire experience less stressful as our attitude was "here's this wonderful opportunity-- look at all this interesting work -- let's just give it a try." We (parents and teacher) definitely kept the focus off achievement and on engagement. That seemed to help the transition a lot.
One added bonus -- the child didn't have time to stress about the situation over the summer. Anticipation is his enemy. Action is his friend.
Good Luck!