The "Ace Attorney"/"Gyakuten Saiban" series is the standard for point-and-click adventure games on the Nintendo DS, and will likely remain that for a long while. However, if Aksys keeps pushing this series, mystery lovers may very well have a nice alternative to the comedic and frantic world of Capcom's flagship franchise with the hard-boiled, dead-pan tales of detective Jake Hunter.
I suppose the first thing I should tell any prospective players is this: if you love the "Ace Attorney" franchise for it's zany, over the top plots and frequent comic relief, you're not going to like this game one bit. Taking everything with a serious tone and a gritty demeanor, "Memories of the Past" is the closest the DS has to a visual novel noir. Even though some cases may come across as a bit outlandish, they always revolve around darker, more sinister sub-plots. For example, whereas Phoenix Wright or Apollo Justice would go about finding information in the most squeaky-clean way possible, Jake Hunter sidesteps that and goes straight to his gang boss informant friend. Hunter may be tracking down criminals, but he also knows how to use some of them to his advantage.
As far as the gameplay goes, it's all a relatively simple affair. Read text, point on a menu with stylus, read more text, rinse, repeat. There is no actual challenge in this game, because you cannot lose. No matter what decision you make, the narrative is always going to somehow work it's way back on track without you having to give any effort. Some players may criticize this gameplay for being too easy, but with "Memories of the Past", it's not about the gameplay; it's about the plot. There's something comforting in spending an hour or so reading through a case like you would a good novel.
The rest of the game is very well put together. Music is great, and the main title theme will probably be lodged in your head for weeks (speaking from experience here.) Graphics are pretty good for what they are (static characters in static backgrounds), and the character designs are excellent (the Japanese artist, Katsuya Terada of "Blood the Last Vampire" fame, has been the designer of characters for every entry in the series.)
However, players of the FIRST Jake Hunter game should be warned about the plot in this entry. Besides the main case and two others, the remainder of the chapters are actually "remasters" of the original cases seen in "Jake Hunter: Detective Story." For new players, this is a lot of bang for the buck, and helps provide insight into the main case; for returning fans (such as myself), it comes across as a bit of a rip-off. Granted, the rest of the cases are new to American shores, and even the remastered ones have new English scripts which flow a lot better than the slightly awkward translations which haunted the first game, but still: it would've been nice to see some of the other cases available to Japanese players.
If you like your detectives hard-boiled, and aren't too weary of games which you can't lose at, then "Jake Hunter Detective Story: Memories of the Past" is some of the most fun you can have on your DS. I would recommend this to anyone looking for a good mystery to last them for a nice while.