For the most part, it's always wise to promote as soon as you can so there will be no repercussions. This is because unless you show one specific unit some serious preferences over others, it's highly unlikely you'll ever reach their max level at their highest possible tier before the end of the game. Mercenaries should especially be promoted once available, as they have no worries about running out of level ups.
Promoting earlier also makes the benefits of promotion far better, as the stat boosts a unit gets upon promotion depends solely on their stats when they are promoted. Instead of receiving a static amount of increases, their stats are instead brought up to the base stats of their promoted class if they are lower. One example of this is seen when promoting Villagers to Mercenaries, when their speed will automatically jump to a Base 10 Speed no matter what their Speed Stat was before they were promoted.
One exception a player should consider is when it comes to Alm Celica. As the main characters of the game, they are much more likely to be used compared to other characters, meaning you have a real shot of reaching Level 20 with their given units. These two also have excellent growth rates when they stack up to others, which makes it all the more wise to wait until Level 20 before promoting them.