We conducted a search for Be star candidates in open clusters using Hα imaging photometry of the Palomar Transient Factory Survey to investigate some connections among Be star phenomena, cluster environments, and ages. Stellar members of clusters were identified by spatial distributions, near-infrared magnitudes and colors, and by proper motions. Among 104 open clusters, we identified 96 Be star candidates in 32 clusters; 11 of our candidates have been reported in previous studies. We found that the clusters with age 7.5 < log(t(year))  8.5 tend to have more Be star candidates; there is about a 40% occurrence rate within this age bin. The clusters in this age bin also tend to have a higher Be fraction N(Be)/N(Be+B-type). These results suggest that the environments of young and intermediate clusters are favorable to the formation of Be phenomena. Spatial distribution of Be star candidates with different ages implies that they do not form preferentially in the central regions. Furthermore, we showed that the mid-infrared (MIR) colors of the Be star candidates are similar to known Be stars, which could be caused by free-free emission or bound-free emission. Some Be star candidates might have no circumstellar dust according to their MIR colors. Finally, among 96 Be candidates, we discovered that one Be star candidate FSR 0904-1 exhibits long-term variability on the timescale of ∼2000 days with an amplitude of 0.2-0.3 mag, indicating a long timescale of disk evolution.