I have find out how to solve one of the problems. To avoid the MMC get corrupted with every 'suspend' it is necessary
to enable CONFIG_MMC_UNSAFE_RESUME in the kernel config.
I have also enabled CONFIG_OMAP_RESET_CLOCKS and some features that were not suspending now are doing it.
There are some other things related to power management there.
Now when suspending I get:

root@overo:/sys/power# echo mem > state
PM: Syncing filesystems ... done.
Freezing user space processes ... (elapsed 0.01 seconds) done.
Freezing remaining freezable tasks ... (elapsed 0.00 seconds) done.
Suspending console(s) (use no_console_suspend to debug)
mmc1: card 0001 removed
Powerdomain (core_pwrdm) didn't enter target state 1
Powerdomain (dss_pwrdm) didn't enter target state 1
Powerdomain (usbhost_pwrdm) didn't enter target state 1
Could not enter target state in pm_suspend
Restarting tasks ... <7>hub 1-0:1.0: state 7 ports 1 chg 0000 evt 0000

The current consumption is now falling to ~242mA when sleeping.

> This sounds like DebugFS. You can find it in menuconfig and then mount
> it yourself.

Yes, it was need to enable it in the kernel, and mount it ( mount -t debugfs debufs /debug).
After enabling ( /sys/power/ ) sleep_while_idle, enable_off_mode and voltage_off_while_idle I get this on the debug:

root@overo:/# cat /debug/pm_debug/count
usbhost_pwrdm (ON),OFF:0,RET:0,INA:0,ON:1
sgx_pwrdm (OFF),OFF:1,RET:0,INA:0,ON:1
per_pwrdm (ON),OFF:773,RET:256,INA:0,ON:1030
dss_pwrdm (ON),OFF:0,RET:4,INA:0,ON:5
cam_pwrdm (OFF),OFF:2,RET:2,INA:0,ON:1
core_pwrdm (ON),OFF:0,RET:0,INA:0,ON:1
neon_pwrdm (ON),OFF:1003,RET:13,INA:89,ON:1106
mpu_pwrdm (ON),OFF:1003,RET:13,INA:89,ON:1106
iva2_pwrdm (OFF),OFF:2,RET:2,INA:0,ON:1
per_clkdm->per_pwrdm (9)
usbhost_clkdm->usbhost_pwrdm (3)
cam_clkdm->cam_pwrdm (0)
dss_clkdm->dss_pwrdm (3)
core_l4_clkdm->core_pwrdm (15)
core_l3_clkdm->core_pwrdm (5)
d2d_clkdm->core_pwrdm (0)
sgx_clkdm->sgx_pwrdm (0)
iva2_clkdm->iva2_pwrdm (0)
neon_clkdm->neon_pwrdm (0)
mpu_clkdm->mpu_pwrdm (0)
virt_opp_clkdm->wkup_pwrdm (0)
prm_clkdm->wkup_pwrdm (10)
cm_clkdm->core_pwrdm (4)

Somebody has an idea about where else I should look to disable these thing on sleep mode?

> > PS.: Another another less important thing but very anoying is everytime
> > when starting to write something in the console appears an strange
> > character (�).
> Not clear on this one. Try connecting with just screen. I use:
> screen /dev/ttyUSB0 115200 8N1
> --Pat

Same thing connecting this way or with kermit. Sometimes the communication brokes some seconds after boot. I think is something wrong with the kernel. When running linux-omap3-2.6.34 it works fine.