As already mentioned, the answer to your question really depends on the med in question. Some have narrow therapeutic indices which can increase the likelihood (and possible severity) of side effects.
As a starting point, check the patient information leaflet for any guidance regarding missed doses. Failing that, tap up your pharmacist for advice.
Going forward, to help avoid missed doses, yeah dossette boxes can be a great help, but that is dependant on the stability of drugs in compliance aids. Some can go in there no problems, others are a big no no for such devices. As an alternative, perhaps ask if your meds come in calender packs ie the days of the week marked on the reverse of the blister.
There are many ways to help to maintain compliance, including apps so it may be worth having a chat with your pharmacist if this is proving an issue.