If you send us the link to the dog, we can point out any red flags (or otherwise) in the description. Certain 'rescue charities' are pretty poor when it comes to being honest about problems with their dogs.
But you should be asking: does the dog have any health issues and/or skin issues, has the dog exhibited any behavioural issues (resource guarding, separation anxiety, shadow chasing, any sort of nervousness around anything 'normal', any fear based aggression, any aggression, barking or howling, destructive behaviour etc).
Is it an escape artist? How well trained is it? What does it eat? What sort of exercise can it handle? What is it like around other dogs? What is it like around cats? Why was it relinquished? How have they checked the suitability of the dog for your home? I.E have they thoroughly checked it around children and in a home environment? How long has the dog been in kennels (or foster if it is in foster).
Depending on the age of your child, I would avoid rescuing - there's another thread at the moment where the OP bought home a rescue dog and wasn't informed it had a (very serious) behavioural issue and it has already bitten her/someone in the house four times in a week. Sadly, not uncommon with rescuing.
Rescues like to...withhold key bits of information when re-homing dogs or just downright lie or sugar-coat the truth to shift dogs out more quickly. Ironic, really, given how hard rescuing can be.