Сергій, thanks for the hint, obexftp still fails for me while, but obexfs actually works.
gandalfthegrey:~# obexftp -b 3c:5a:37:83:7f:2a -l
Browsing 3c:5a:37:83:7f:2a ...
Connecting...failed: connect
Tried to connect for 2ms
The user may have rejected the transfer: Connection refused
gandalfthegrey:~# mount -t fuse "obexfs#-b3C:5A:37:83:7F:2A" /mnt/mnt
gandalfthegrey:~# 

bluetooth-applet browse files still does not work (it used to).

Ok, now I have something very interesting: I have a custom app that talks over bluetooth and it wasn't working.
It was getting:
> ACL data: handle 12 flags 0x02 dlen 16
    L2CAP(s): Connect rsp: dcid 0x0000 scid 0x0041 result 3 status 0 Connection refused - security block

Now, if I use mount -t fuse obexfs first, I can browse my files and my
other bluetooth app also starts working magically.
It seems that fuse manages to do auth better than other apps like obexftp
and my custom app, and once that auth has been done, other things just happen to work.

As soon as I unmount fuse/obexfs, then things stop working agagin.
Clearly, it does something better than the other apps and once it has authed with my phone, other things start working.

< HCI Command: Create Connection (0x01|0x0005) plen 13
    bdaddr 3C:5A:37:83:7F:2A ptype 0xcc18 rswitch 0x01 clkoffset 0x0000
    Packet type: DM1 DM3 DM5 DH1 DH3 DH5 
> HCI Event: Command Status (0x0f) plen 4
    Create Connection (0x01|0x0005) status 0x00 ncmd 1
> HCI Event: Connect Complete (0x03) plen 11
    status 0x00 handle 12 bdaddr 3C:5A:37:83:7F:2A type ACL encrypt 0x00
< HCI Command: Read Remote Supported Features (0x01|0x001b) plen 2
    handle 12
> HCI Event: Command Status (0x0f) plen 4
    Read Remote Supported Features (0x01|0x001b) status 0x00 ncmd 1
> HCI Event: Read Remote Supported Features (0x0b) plen 11
    status 0x00 handle 12
    Features: 0xbf 0xfe 0x8f 0xfe 0x9b 0xff 0x79 0x83
< HCI Command: Read Remote Extended Features (0x01|0x001c) plen 3
    handle 12 page 1
> HCI Event: Command Status (0x0f) plen 4
    Read Remote Extended Features (0x01|0x001c) status 0x00 ncmd 1
> HCI Event: Max Slots Change (0x1b) plen 3
    handle 12 slots 5
> HCI Event: Read Remote Extended Features (0x23) plen 13
    status 0x00 handle 12 page 1 max 1
    Features: 0x01 0x00 0x00 0x00 0x00 0x00 0x00 0x00
< HCI Command: Remote Name Request (0x01|0x0019) plen 10
    bdaddr 3C:5A:37:83:7F:2A mode 2 clkoffset 0x0000
< ACL data: handle 12 flags 0x00 dlen 10
    L2CAP(s): Info req: type 2
> HCI Event: Command Status (0x0f) plen 4
    Remote Name Request (0x01|0x0019) status 0x00 ncmd 1
> ACL data: handle 12 flags 0x02 dlen 16
    L2CAP(s): Info rsp: type 2 result 0
      Extended feature mask 0x00b8
< ACL data: handle 12 flags 0x00 dlen 10
    L2CAP(s): Info req: type 3
> ACL data: handle 12 flags 0x02 dlen 20
    L2CAP(s): Info rsp: type 3 result 0
      Fixed channel list
< ACL data: handle 12 flags 0x00 dlen 12
    L2CAP(s): Connect req: psm 1 scid 0x0040
> ACL data: handle 12 flags 0x02 dlen 16
    L2CAP(s): Connect rsp: dcid 0x0040 scid 0x0040 result 1 status 0
      Connection pending - No futher information available
> ACL data: handle 12 flags 0x02 dlen 10
    L2CAP(s): Info req: type 2
< ACL data: handle 12 flags 0x00 dlen 16
    L2CAP(s): Info rsp: type 2 result 0
      Extended feature mask 0x00b8
> ACL data: handle 12 flags 0x02 dlen 10
    L2CAP(s): Info req: type 3
< ACL data: handle 12 flags 0x00 dlen 20
    L2CAP(s): Info rsp: type 3 result 0
      Fixed channel list
> ACL data: handle 12 flags 0x02 dlen 16
    L2CAP(s): Connect rsp: dcid 0x0040 scid 0x0040 result 0 status 0
      Connection successful

There you go, it got through.

Are there other simple apps to debug connections?