I couldn't find any information on an "Aston Martin Valiant". It's possible that it may be a made-up or non-existent model.
However, if you're referring to the Dodge Valiant, here is a list of potential issues in order from most common to least rare based on various sources:
Rust and corrosion (door sills, trunk floor, wheel wells)
Transmission problems (slipping, hesitation, failure to engage gears)
Brake wear and noise (spongy brake pedal, grinding or squealing noises)