Save files for 'Tokimeki Memorial: Forever With You' with four playthroughs completed, which should be enough to trigger additional dialogue in Policenauts. From the readme for the English fan translation patch of Policenauts:

"Also like the PlayStation version, if you have save data from the game Tokimeki Memorial: Forever With You, the game will insert additional dialogue into a handful of conversations, depending on how you played Tokimeki Memorial. This consists of throwaway jokes that imagine Jonathan Ingram as being the protagonist in Tokimeki Memorial. Though as of this writing no English translation patch for the Saturn (or PlayStation) version of Tokimeki Memorial: Forever With You is available, like the PlayStation patch we future-proofed the patch by translating this dialogue as well."

Bonus content can be accessed by selecting the bottom item in the main menu, which will take you to another menu with the following options:

1. Mini-games
 - TwinBee Time Attack
 - PSYTH
 - 100-metre Dash
 - Goldfish Scooping
 - Ring Toss

2. Free Talk

3. Endings
 - Bad ending
 - Miharu Tatebayashi
 - Rei Ijuuin
 - Yuina Himoo
 - Yukari Koshiki