You have two questions here really, how can you improve communication and should you bring it up with your manager and if so how. I'll answer them separately.
How to improve communications
It sounds like you have almost no communication between people. The most obvious way to fix this is just to try and establish a culture of asking people what they're doing, encouraging people to share. But if that's not something that's happening you need some framework around it.
Team meetings: Regular team meetings are an easy way to do this. They can be monthly, weekly, even daily depending on the project timelines and team size. In general weekly is common -- the team comes together at a fixed time, each person says what they've done since last meeting, what they're doing next and what issues they're facing. It's an open sharing discussion -- have someone take minutes and store them somewhere.
This can be a meeting the manager attends, where it also functions as a status report. Or it can just be the team doing more 'information sharing'.
Peer reviews: Having someone else look over your code / design / work, whatever is useful in two ways. First the second set of eyes will likely catch things you missed, and also now someone else knows what you're doing and why. Rotate who's involved in what review and rapidly the whole team has a wider understanding of everyone's project. The time spend to do this is recouped in the time saved by avoiding the problems you detail. This does require a culture shift, and there will be resistance, but in general -- once the benefits become clear -- then people come around. I'm assuming your in software but the same system works for any engineering/creative task, there are plenty of online resources and articles about peer reviews.
Documentation: Do you have documentation when a project is handed over? It sounds like you don't, which seems to be a problem. Or perhaps the documentation is not good enough. Either review documentation as well, or create templates to guide people into including the correct information, or have some sort of handover checklist where the supplier and receiver have to both agree everything required is there.
Use your tools: Again, assuming software. Do you have a source code control system? (If not, you really should!). Can you build notifications into that so everyone can see each others commits? Or generate weekly reports? Just something to give an insight into what is going on.
Should you bring it up with your manager and if so how
You should definitely bring it up -- it's affecting your productivity and it's a chance to make things better for everyone. And decent manager wants to hear that sort of input -- as long as you're not just whining about it. And, if they decide not to change things, you accept that and move on (or come up with other suggestions).
As I've said in answers elsewhere, don't just say "this is a problem" go to your manager with solutions. Say "I think we should try this or this, because it would help us avoid these problems in the future". The suggestions above will help with what you solutions you give (you'll know what will work best) and you can do find some 'best practice' on line to give you backup for why it will work.
Suggest it as a trial, "Why don't we do something for six months and see what happens".
It's not clear if this is your first job, if not you can go to the "At my previous company we started doing team meetings and found it really useful at avoiding problems such as X, Y and Z". If you don't have a previous company you can do the same but "My friend works for a similar company and they've started doing ..." or even "At college/university a tutor was recommending ..." or just "I was doing research on how other companies avoid problems like X, Y and Z and found a lot of people recommending ...". Or just say some guy called SpaceDog on the internet suggested it, but that might not get you as far ... :)
Be careful with the above if you're saying it's something that's done elsewhere when that's not true and it's something they can check as it'll hurt your credibility and your case. But if you use the friend argument without specifying which friend or which company it's pretty much unfalsifiable -- and my suggests above are standard practice at a great many companies.
