Strengths:
This is a highly controlled clinical method of obtaining data and Fisher and her colleagues checked objectivity at every stage of the procedure.
Identification of the reward centres of the brain support the idea that human beings may have an evolved brain system which ensures that they become 'hooked' on an individual, which increases the possibility of them reproducing.
The standardised procedure means that the study is replicable, which increases its reliability.
Limitations
The small sample size of 17 participants means that the results are not very meaningful and may not be robust in terms of statistical analysis.
The sample comprised relatively young students from the same university, which also limits generalisability.
Additionally, it is overly reductionist to use brain scans to determine how romantic love is experienced: there may be a range of other factors involved, such as similarity, same upbringing, shared ideals, cultural influences.
So little is really known about the brain that there may be other explanations for the activation of the reward centres during the fMRI scan - perhaps the participants were simply excited to be in a brain scanner for the first time and this stimulated the dopamine-rich areas.
Scanning participants' brains is clearly an artificial task, which means that the results are low in ecological validity. Use of fMRI scans is also an expensive way to collect data, which is possibly why the sample is so small.