interface Ethernet0/0
ip address 10.0.0.2 255.255.255.0
ip access-group 100 in
ip access-group 101 out
half-duplex
!
interface Serial0/0
ip address 192.168.0.2 255.255.255.0
ip access-group 102 out
! 


changes  you need to perform  **************************

1.- remove acccess-group 101 out from ethernet0/0
2.- remove entry - permit ip any host 10.0.0.3 - from access-list 100 so it reads:

access-list 100 permit ip host 10.0.0.3 any
access-list 100 permit icmp host 10.0.0.1 host 192.168.0.1 log-input
access-list 100 permit tcp host 10.0.0.1 host 192.168.0.1 log-input
access-list 100 deny ip any any

3.- modify access-list 102 so that it reads:

 access-list 102 permit icmp any any administratively-prohibited log-input
 access-list 102 permit icmp any any echo log-input
 access-list 102 permit icmp any any echo-reply log-input
 access-list 102 permit icmp any any packet-too-big log-input 
 access-list 102 permit icmp any any time-exceeded log-input
 access-list 102 permit icmp any any traceroute log-input
 access-list 102 permit icmp any any unreachable log-input
 access-list 102 permit ip any host 10.0.0.3 
 access-list 102 deny ip any any

also you might want to add these entries at the beginning of the ACL 102 for anti spoofing attacks
 
 access-list 102 deny ip 127.0.0.0 0.255.255.255 any
 access-list 102 deny ip 10.0.0.0 0.0.0.255 any

4.- Apply access list 102 to serial interface on the INBOUND direction
    ip access-group 102 in

5.- remove the inspection instruction from teh serial interface
    no ip inspect http_out <direction>

6.- Apply inspection to the Ethernet0/0 interface in the Inbound direction
    ip inspect http_out in

7.- Test by initiating some http, icmp, udp traffic from 10.0.0.3 to outside