As with all functions, I think it manifests a little differently depending on where it is in the function order and what other functions is is mostly interacting with. In the case of an INFP, it is the tertiary function so it would not be as developed and dominant as in an ISxJ but it should also not be insignificant as well.
In my case, I relate fairly strongly to the description of quickly being able to notice things that are out of place (its usually "something does not feel right" and then a followup validates that suspicion) so I think that aspect of it in me is working at a subconscious level. Catching typos (other than my own of course

) is the most common ocurance of that for me, but walking into a location I have not been for a long time and noticing that things have moved or changed (sometimes even minor stuff) when nobody else with me notices the same things is another manifestation of it that still happens often enough to be memorable.
My short term memory is absolutly horrible to the point that I've rightfuly been called "absent minded" - "Gah! where did I put that pen!", "oh, its already in my hand, that explains why it wasn't where I thought I would have left it", but I can often recall things in great detail from my childhood that neither my sister (who is older than I) or my parents do "remember when you (recolection of specific event or activity) back when I would have been about 5 or 6 (or similar age for example)"). In general, the more meaning somethign has to me personally, the stronger the memory is, but I also have my share of long term memories that seem fairly meaningless to me too. One specific diference is that in meaningful memories, conversations, emotions and the environment they took place in are the strongest part of the memory (recalling a conversation at a specific resturant, what was talked about and how it made me feel and such), and in the less meaningful ones, things like the weather, time of day and other more sensory things like that are the bigger part of the memory (recalling a childhood trip to a waterpark (somewhere between 20-25 years ago)), what slides I went on, which were my favourite, what the weather was like, what the layout of the park was like, what I got for lunch, and so on.
I would further add that my memory with fact based stuff is also quite poor. I never could memorize my times tables for instance (but I could calculate them as needed through more basic math on the fly to fake it most fo the time) and needing to memorize minutiae has always been a weak point for me. If I do not have a specific reason to want to know the details, I will quickly forget them and just look them up as needed, but if the facts and details are important to somethign that is important to me, I can often recall them without consciously making an effort to store them in memory.
This is a bit of a tangent to the direct topic of memory, but still pertains to Si, so I think it has some relevance and may be of interest to some readers. This applies more to it as a tertiary function, but here is a short description from INFJorINFP.com regarding Si.
From INFJorINFP.com (by Vicky Jo)
INFJ or INFP? a closer look
INFP Tertiary
Introverted Sensing (Si)
Reviewing
Linking
Comparing and contrasting
Noticing match and mismatch
Past
"This is how it has always been."
"This reminds me of . . ."
...
I compare current experience against stored past impressions and experiences.
OR
I am aware at a detailed level of what is going on in my body, including my emotional state.
...
INFPs are often well rooted in the past, with a good memory of things that have happened historically, and are attracted to "collecting" facts. They sometimes have a strong grasp of family and tradition and may have a great deal of familiarity with their family tree or display an interest in genealogy. They may act as the "family historian" at times, knowing who begat whom and how a particular branch is related. They have long memories. I know one INFP who could recite from memory what year of childhood he first spoke or began walking, including details about what hairstyles he wore at different stages of life! Others like to visit the same places frequently, and let their minds drift back in time to recall previous visits. Nostalgia is often engaged, and they enjoy telling stories from their past. (Introverted Sensing is a cultural norm in the U.S., so it seems fairly "typical" to look to the past this way.) One INFP tells how he enjoys his routines, his habits, doing things by rote. He does the everyday chores of maintaining his home, and these keep him in his comfort zone. Similarly, sometimes INFPs will stay at the same job for years because they're used to it -- even when the job stinks. (A friend of mine stayed at a dreadful job for 9 years!) INFPs sometimes display "body wisdom," and their bodies can be barometers for how they are feeling, whether through illness, food allergies, or headaches. They are often given to taking medications to control their physical being in some fashion. (On a Yahoo Group one time when there was a discussion of medications, it was a veritable drugstore! It seemed every one of them was popping pills to control something.) These are all common ways that Si will manifest in the INFP type code.
I suspect that many INFPs believe they are "J's" because they enjoy the predictability of a routine, and imagine that is "J."
I agree with the nostalgia part of that, but have very little interest in geneology or family history and such - I have some curiosity about what my great great anscestors of the old world were like, but not enough to actualy dig into it and research it. The rest of that description I have mixed feelings about. I would not say I like routines, but I don't hate them either, and the reason for staying at the same job has more to do with factors thaat are nto related to the job itself or even job satisfaction one way or the other. As mentioned in a recent conversation, I like some structure and order to things, but knowing that I have the
option to make changes whenever I want is essential before I can try to become comfortable with a routine way of doing things.