Orsdxy

There are no paradox concerns.

Your system prevents modification of the past, so there is no way to cause changes which would lead you to not go back in time, or go back in time differently.

Your system cannot see into the future, so you cannot see the effects of your actions and act differently.

Really, it's more of a VCR than time travel. You can go back to see the things you previously recorded, and that's it. Also, there's no fast-forward/rewind, just play forwards and play backwards.

Musing about the concept...

Essentially, living memory becomes (potentially) more accessible. The big benefit is that those memories could contain information that was originally not really noticed, but with the hindsight of future knowledge can be 'recalled' and brought forward and acted on.

It creates an interesting new branch of criminal investigations. Witnesses can reveal forgotten details, especially form recent events, leading to more certain rulings.

It creates an interesting new branch of research, for the same reason. With proper incentive, a survivor of Event X (a Kennedy assassination, for example) can potentially bring back forgotten evidence. A WWII survivor could be 'sent back' to try to 'remember'(?) conversations that have since been lost... a conversation with Einstein, or Tesla.

Conversations with native Americans in their own language could (potentially) be recovered -- languages which are inadequately documented and have since gone extinct.

This works for any organization in fact. Crime syndicates can use it (potentially) to better learn the identity of informants. Or, to more easily remember (or notice!) the location of valuables.

I think there is a major flaw:
Since there is no fast forward, you could never catch up with the present. For everyone else, time moves forward and you are always behind.
Unless triggering the time travel freezes time for everyone else.

Yes and no....

Part of time is that not only does the past affect the future, but the future also affects the past.

By going back in time and taking note of the pickpocket, for example, you learn enough about him to file a police report, so you do so.

However, had you not gone into the past to discover what happened to your wallet, you have still changed the future, as you would not have reported it stolen had you not discovered it was stolen and not lost.

So, say instead, you were going to meet a friend for lunch, and in the future, that friend would have dropped his wallet, and lost it at your lunch. Now, he doesn't lose it...

You go back by rewinding, but your conscience does not go backwards? It is actually remembering future events relative to the time you return to you. It's like information travels backwards with you. In the first scenario you can act to undo mistakes and therefore the mistake was never done and there was no reason for the trip - That's already a paradox. In the second scenario, the same things will happen again. That is, you do the same mistakes even though you know it. What prevents you from taking corrective measures? Why, in your example, you would see the pickpocketer and could do nothing about it? Would you be able to see him from a different angle and still be unable to warn your past-yourself? Suppose you stopped your time-rewind and returned to "replay", will you be the "same one", or will another observer see you and your past-you?

If you do it through your mind there is no problem, that's just memory(a very good and also problematic one) or watching a movie in first person of your actions, strap a camera in your head, force yourself to follow this rules and you can do this yourself, but if you do it through external interference like magic or a machine that send you on time, that's a action that happened in the past and you stay trapped on the loop.

To break the loop paradox, you could create a "escape rope", Lets say this.
january 12 of 2019 at 13:00 you press the button to the escape rope, you keep living your life normaly, at january 13 of 2019 at 15:00 you see a murder, then at january 14 of 2019 at 12:00 you rewind time to the january 12 of 2019 at 12:59, you start the loop, then at january 12 of 2019 at 13:00 you press again the "escape rope" that have a command which says "if you are on a loop unmake the effect of the loop button when you press it" (frase it as you like, also yes, I code), when you arrive at january 14 of 2019 at 12:00 you press the button the effect of the escape rope triggers and you break out of the loop.

Your system cannot work with our understanding of physics.

Think of Schrödinger' cat. The effect most people associate to it cannot be reproduced on a macroscopic object such as a cat, but it is reproducible with particles. It is happening at every moment to every subatomic particle. But for the sake of argument, let's call some paint particles on a brick of a wall our cat particles. They can cause the paint to peel off in various patterns; You will only know when you observe them.

You passed by your backyard yesterday without paying attention to a certain brick. Today you notice some paint is peeling off that brick, forming a pattern.

You go back to the "past" to do the wallet finding thing. You think you lost it close to the wall, so now you pay attention to the brick.

The fact that you are observing them on the past means they have to collapse their wave function at that moment, so the universe decides whether and how the paint peels off at that moment. You just changed the past.

You have a paradox now. If the paint must always off to be just as you remember from the "present", then the wave function collapse in the "present" extended to the "past", meaning anything happening in the present affects and changes the "past" retroactively. Otherwise, wave function collapsing from direct "past" observations may cause changes to events anyway, and those changed will accumulate through time a la butterfly effect.